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Canonical Metrics in Kähler Geometry / Gang Tian / Bâle (CHE) ; Boston, MA : Birkhäuser (2000)
Titre : Canonical Metrics in Kähler Geometry Type de document : document électronique Auteurs : Gang Tian ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2000 Collection : Lectures in Mathematics. ETH Zürich Importance : VII, 101 p Présentation : online resource ISBN/ISSN/EAN : 978-3-0348-8389-4 Langues : Anglais (eng) Tags : Mathematics Global analysis Manifolds Differential geometry Physics Differential Geometry Global Analysis and Analysis on Manifolds Mathematical Methods in Physics Note de contenu : 1 Introduction to Kähler manifolds -- 1.1 Kähler metrics -- 1.2 Curvature of Kähler metrics -- 2 Extremal Kähler metrics -- 2.1 The space of Kähler metrics -- 2.2 A brief review of Chern classes -- 2.3 Uniformization of Kähler-Einstein manifolds -- 3 Calabi-Futaki invariants -- 3.1 Definition of Calabi-Futaki invariants -- 3.2 Localization formula for Calabi-Futaki invariants -- 4 Scalar curvature as a moment map -- 5 Kähler-Einstein metrics with non-positive scalar curvature -- 5.1 The Calabi-Yau Theorem -- 5.2 Kähler-Einstein metrics for manifolds with c1(M) < 0 -- 6 Kähler-Einstein metrics with positive scalar curvature -- 6.1 A variational approach -- 6.2 Existence of Kähler-Einstein metrics -- 6.3 Examples -- 7 Applications and generalizations -- 7.1 A manifold without Kähler-Einstein metric -- 7.2 K-energy and metrics of constant scalar curvature -- 7.3 Relation to stability Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128117 Canonical Metrics in Kähler Geometry [document électronique] / Gang Tian ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2000 . - VII, 101 p : online resource. - (Lectures in Mathematics. ETH Zürich) .
ISBN : 978-3-0348-8389-4
Langues : Anglais (eng)
Tags : Mathematics Global analysis Manifolds Differential geometry Physics Differential Geometry Global Analysis and Analysis on Manifolds Mathematical Methods in Physics Note de contenu : 1 Introduction to Kähler manifolds -- 1.1 Kähler metrics -- 1.2 Curvature of Kähler metrics -- 2 Extremal Kähler metrics -- 2.1 The space of Kähler metrics -- 2.2 A brief review of Chern classes -- 2.3 Uniformization of Kähler-Einstein manifolds -- 3 Calabi-Futaki invariants -- 3.1 Definition of Calabi-Futaki invariants -- 3.2 Localization formula for Calabi-Futaki invariants -- 4 Scalar curvature as a moment map -- 5 Kähler-Einstein metrics with non-positive scalar curvature -- 5.1 The Calabi-Yau Theorem -- 5.2 Kähler-Einstein metrics for manifolds with c1(M) < 0 -- 6 Kähler-Einstein metrics with positive scalar curvature -- 6.1 A variational approach -- 6.2 Existence of Kähler-Einstein metrics -- 6.3 Examples -- 7 Applications and generalizations -- 7.1 A manifold without Kähler-Einstein metric -- 7.2 K-energy and metrics of constant scalar curvature -- 7.3 Relation to stability Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128117 Cardinal Functions on Boolean Algebras / J. Donald Monk / Bâle (CHE) ; Boston, MA : Birkhäuser (1990)
Titre : Cardinal Functions on Boolean Algebras Type de document : document électronique Auteurs : J. Donald Monk ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 1990 Collection : Lectures in Mathematics. ETH Zürich Importance : VII, 153 p Présentation : online resource ISBN/ISSN/EAN : 978-3-0348-6381-0 Langues : Anglais (eng) Tags : Science Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127984 Cardinal Functions on Boolean Algebras [document électronique] / J. Donald Monk ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 1990 . - VII, 153 p : online resource. - (Lectures in Mathematics. ETH Zürich) .
ISBN : 978-3-0348-6381-0
Langues : Anglais (eng)
Tags : Science Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127984 Compact Riemann Surfaces / Raghavan Narasimhan / Bâle (CHE) ; Boston, MA : Birkhäuser (1992)
Titre : Compact Riemann Surfaces Type de document : document électronique Auteurs : Raghavan Narasimhan ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 1992 Collection : Lectures in Mathematics. ETH Zürich Importance : VI, 122 p. 2 illus Présentation : online resource ISBN/ISSN/EAN : 978-3-0348-8617-8 Langues : Anglais (eng) Tags : Mathematics Mathematical analysis Analysis Note de contenu : 1. Algebraic functions -- 2. Riemann surfaces -- 3. The sheaf of germs of holomorphic functions -- 4. The Riemann surface of an algebraic function -- 5. Sheaves -- 6. Vector bundles, line bundles and divisors -- 7. Finiteness theorems -- 8. The Dolbeault isomorphism -- 9. Weyl?s lemma and the Serre duality theorem -- 10. The Riemann-Roch theorem and some applications -- 11. Further properties of compact Riemann surfaces -- 12. Hyperelliptic curves and the canonical map -- 13. Some geometry of curves in projective space -- 14. Bilinear relations -- 15. The Jacobian and Abel?s theorem -- 16. The Riemann theta function -- 17. The theta divisor -- 18. Torelli?s theorem -- 19. Riemann?s theorem on the singularities of ? Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128166 Compact Riemann Surfaces [document électronique] / Raghavan Narasimhan ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 1992 . - VI, 122 p. 2 illus : online resource. - (Lectures in Mathematics. ETH Zürich) .
ISBN : 978-3-0348-8617-8
Langues : Anglais (eng)
Tags : Mathematics Mathematical analysis Analysis Note de contenu : 1. Algebraic functions -- 2. Riemann surfaces -- 3. The sheaf of germs of holomorphic functions -- 4. The Riemann surface of an algebraic function -- 5. Sheaves -- 6. Vector bundles, line bundles and divisors -- 7. Finiteness theorems -- 8. The Dolbeault isomorphism -- 9. Weyl?s lemma and the Serre duality theorem -- 10. The Riemann-Roch theorem and some applications -- 11. Further properties of compact Riemann surfaces -- 12. Hyperelliptic curves and the canonical map -- 13. Some geometry of curves in projective space -- 14. Bilinear relations -- 15. The Jacobian and Abel?s theorem -- 16. The Riemann theta function -- 17. The theta divisor -- 18. Torelli?s theorem -- 19. Riemann?s theorem on the singularities of ? Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128166 Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems / Frédéric Hélein / Bâle (CHE) ; Boston, MA : Birkhäuser (2001)
Titre : Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems Type de document : document électronique Auteurs : Frédéric Hélein ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2001 Collection : Lectures in Mathematics. ETH Zürich Importance : 122 p Présentation : online resource ISBN/ISSN/EAN : 978-3-0348-8330-6 Langues : Anglais (eng) Tags : Mathematics Geometry Note de contenu : 1 Introduction: Surfaces with prescribed mean curvature -- 2 From minimal surfaces and CMC surfaces to harmonic maps -- 2.1 Minimal surfaces -- 2.2 Constant mean curvature surfaces -- 3 Variational point of view and Noether?s theorem -- 4 Working with the Hopf differential -- 4.1 Appendix -- 5 The Gauss-Codazzi condition -- 5.1 Appendix -- 6 Elementary twistor theory for harmonic maps -- 6.1 Appendix -- 7 Harmonic maps as an integrable system -- 7.1 Maps into spheres -- 7.2 Generalizations -- 7.3 A new setting: loop groups -- 7.4 Examples -- 8 Construction of finite type solutions -- 8.1 Preliminary: the Iwasawa decomposition (for). -- 8.2 Application to loop Lie algebras -- 8.3 The algorithm -- 8.4 Some further properties of finite type solutions -- 9 Constant mean curvature tori are of finite type -- 9.1 The result -- 9.2 Appendix -- 10 Wente tori -- 10.1 CMC surfaces with planar curvature lines -- 10.2 A system of commuting ordinary equations -- 10.3 Recovering a finite type solution -- 10.4 Spectral curves -- 11 Weierstrass type representations -- 11.1 Loop groups decompositions -- 11.2 Solutions in terms of holomorphic data -- 11.3 Meromorphic potentials -- 11.4 Generalizations Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128107 Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems [document électronique] / Frédéric Hélein ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2001 . - 122 p : online resource. - (Lectures in Mathematics. ETH Zürich) .
ISBN : 978-3-0348-8330-6
Langues : Anglais (eng)
Tags : Mathematics Geometry Note de contenu : 1 Introduction: Surfaces with prescribed mean curvature -- 2 From minimal surfaces and CMC surfaces to harmonic maps -- 2.1 Minimal surfaces -- 2.2 Constant mean curvature surfaces -- 3 Variational point of view and Noether?s theorem -- 4 Working with the Hopf differential -- 4.1 Appendix -- 5 The Gauss-Codazzi condition -- 5.1 Appendix -- 6 Elementary twistor theory for harmonic maps -- 6.1 Appendix -- 7 Harmonic maps as an integrable system -- 7.1 Maps into spheres -- 7.2 Generalizations -- 7.3 A new setting: loop groups -- 7.4 Examples -- 8 Construction of finite type solutions -- 8.1 Preliminary: the Iwasawa decomposition (for). -- 8.2 Application to loop Lie algebras -- 8.3 The algorithm -- 8.4 Some further properties of finite type solutions -- 9 Constant mean curvature tori are of finite type -- 9.1 The result -- 9.2 Appendix -- 10 Wente tori -- 10.1 CMC surfaces with planar curvature lines -- 10.2 A system of commuting ordinary equations -- 10.3 Recovering a finite type solution -- 10.4 Spectral curves -- 11 Weierstrass type representations -- 11.1 Loop groups decompositions -- 11.2 Solutions in terms of holomorphic data -- 11.3 Meromorphic potentials -- 11.4 Generalizations Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128107 Convergence of Iterations for Linear Equations / Olavi Nevanlinna / Bâle (CHE) ; Boston, MA : Birkhäuser (1993)
Titre : Convergence of Iterations for Linear Equations Type de document : document électronique Auteurs : Olavi Nevanlinna ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 1993 Collection : Lectures in Mathematics. ETH Zürich Importance : VIII, 180 p. 15 illus Présentation : online resource ISBN/ISSN/EAN : 978-3-0348-8547-8 Langues : Anglais (eng) Tags : Science Résumé : Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and focuses on the dynamical aspects of the iteration processes. For example, there are many similarities between the evolution of a Krylov subspace process and that of linear operator semigroups, in particular in the beginning of the iteration. A lifespan of an iteration might typically start with a fast but slowing phase. Such a behavior is sublinear in nature, and is essentially independent of whether the problem is singular or not. Then, for nonsingular problems, the iteration might run with a linear speed before a possible superlinear phase. All these phases are based on different mathematical mechanisms which the book outlines. The goal is to know how to precondition effectively, both in the case of "numerical linear algebra" (where one usually thinks of first fixing a finite dimensional problem to be solved) and in function spaces where the "preconditioning" corresponds to software which approximately solves the original problem Note de contenu : 1. Motivation, problem and notation -- 1.1 Motivation -- 1.2 Problem formulation -- 1.3 Usual tools -- 1.4 Notation for polynomial acceleration -- 1.5 Minimal error and minimal residual -- 1.6 Approximation of the solution operator -- 1.7 Location of zeros -- 1.8 Heuristics -- Comments to Chapter 1 -- 2. Spectrum, resolvent and power boundedness -- 2.1 The spectrum -- 2.2 The resolvent -- 2.3 The spectral mapping theorem -- 2.4 Continuity of the spectrum -- 2.5 Equivalent norms -- 2.6 The Yosida approximation -- 2.7 Power bounded operators -- 2.8 Minimal polynomials and algebraic operators -- 2.9 Quasialgebraic operators -- 2.10 Polynomial numerical hull -- Comments to Chapter 2 -- 3. Linear convergence -- 3.1 Preliminaries -- 3.2 Generating functions and asymptotic convergence factors -- 3.3 Optimal reduction factor -- 3.4 Green?s function for G? -- 3.5 Optimal polynomials for -- 3.6 Simply connected G?(L) -- 3.7 Stationary recursions -- 3.8 Simple examples -- Comments to Chapter 3 -- 4. Sublinear convergence -- 4.1 Introduction -- 4.2 Convergence of Lk(L?1) -- 4.3 Splitting into invariant subspaces -- 4.4 Uniform convergence -- 4.5 Nonisolated singularity and successive approximation -- 4.6 Nonisolated singularity and polynomial acceleration -- 4.7 Fractional powers of operators -- 4.8 Convergence of iterates -- 4.9 Convergence with speed -- Comments to Chapter 4 -- 5. Superlinear convergence -- 5.1 What is superlinear -- 5.2 Introductory examples -- 5.3 Order and type -- 5.4 Finite termination -- 5.5 Lower and upper bounds for optimal polynomials -- 5.6 Infinite products -- 5.7 Almost algebraic operators -- 5.8 Estimates using singular values -- 5.9 Multiple clusters -- 5.10 Approximation with algebraic operators -- 5.11 Locally superlinear implies superlinear -- Comments to Chapter 5 -- References -- Definitions Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128146 Convergence of Iterations for Linear Equations [document électronique] / Olavi Nevanlinna ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 1993 . - VIII, 180 p. 15 illus : online resource. - (Lectures in Mathematics. ETH Zürich) .
ISBN : 978-3-0348-8547-8
Langues : Anglais (eng)
Tags : Science Résumé : Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and focuses on the dynamical aspects of the iteration processes. For example, there are many similarities between the evolution of a Krylov subspace process and that of linear operator semigroups, in particular in the beginning of the iteration. A lifespan of an iteration might typically start with a fast but slowing phase. Such a behavior is sublinear in nature, and is essentially independent of whether the problem is singular or not. Then, for nonsingular problems, the iteration might run with a linear speed before a possible superlinear phase. All these phases are based on different mathematical mechanisms which the book outlines. The goal is to know how to precondition effectively, both in the case of "numerical linear algebra" (where one usually thinks of first fixing a finite dimensional problem to be solved) and in function spaces where the "preconditioning" corresponds to software which approximately solves the original problem Note de contenu : 1. Motivation, problem and notation -- 1.1 Motivation -- 1.2 Problem formulation -- 1.3 Usual tools -- 1.4 Notation for polynomial acceleration -- 1.5 Minimal error and minimal residual -- 1.6 Approximation of the solution operator -- 1.7 Location of zeros -- 1.8 Heuristics -- Comments to Chapter 1 -- 2. Spectrum, resolvent and power boundedness -- 2.1 The spectrum -- 2.2 The resolvent -- 2.3 The spectral mapping theorem -- 2.4 Continuity of the spectrum -- 2.5 Equivalent norms -- 2.6 The Yosida approximation -- 2.7 Power bounded operators -- 2.8 Minimal polynomials and algebraic operators -- 2.9 Quasialgebraic operators -- 2.10 Polynomial numerical hull -- Comments to Chapter 2 -- 3. Linear convergence -- 3.1 Preliminaries -- 3.2 Generating functions and asymptotic convergence factors -- 3.3 Optimal reduction factor -- 3.4 Green?s function for G? -- 3.5 Optimal polynomials for -- 3.6 Simply connected G?(L) -- 3.7 Stationary recursions -- 3.8 Simple examples -- Comments to Chapter 3 -- 4. Sublinear convergence -- 4.1 Introduction -- 4.2 Convergence of Lk(L?1) -- 4.3 Splitting into invariant subspaces -- 4.4 Uniform convergence -- 4.5 Nonisolated singularity and successive approximation -- 4.6 Nonisolated singularity and polynomial acceleration -- 4.7 Fractional powers of operators -- 4.8 Convergence of iterates -- 4.9 Convergence with speed -- Comments to Chapter 4 -- 5. Superlinear convergence -- 5.1 What is superlinear -- 5.2 Introductory examples -- 5.3 Order and type -- 5.4 Finite termination -- 5.5 Lower and upper bounds for optimal polynomials -- 5.6 Infinite products -- 5.7 Almost algebraic operators -- 5.8 Estimates using singular values -- 5.9 Multiple clusters -- 5.10 Approximation with algebraic operators -- 5.11 Locally superlinear implies superlinear -- Comments to Chapter 5 -- References -- Definitions Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128146 Counting, Sampling and Integrating: Algorithm and Complexity / Mark Jerrum / Bâle (CHE) ; Boston, MA : Birkhäuser (2003)
PermalinkGradient Flows / Luigi Ambrosio / Bâle (CHE) ; Boston, MA : Birkhäuser (2005)
PermalinkGradient Flows / Luigi Ambrosio / Bâle (CHE) ; Boston, MA : Birkhäuser (2008)
PermalinkHyperbolic Systems of Conservation Laws / Philippe G. LeFloch / Bâle (CHE) ; Boston, MA : Birkhäuser (2002)
PermalinkIntroduction to Combinatorial Torsions / Vladimir Turaev / Bâle (CHE) ; Boston, MA : Birkhäuser (2001)
PermalinkIntroduction to the Baum-Connes Conjecture / Alain Valette / Bâle (CHE) ; Boston, MA : Birkhäuser (2002)
PermalinkMarkov Processes and Differential Equations / Mark I. Freidlin / Bâle (CHE) ; Boston, MA : Birkhäuser (1996)
PermalinkModules and Algebras / Jon F. Carlson / Bâle (CHE) ; Boston, MA : Birkhäuser (1996)
PermalinkNonpositive Curvature: Geometric and Analytic Aspects / Jürgen Jost / Bâle (CHE) ; Boston, MA : Birkhäuser (1997)
PermalinkNumerical Methods for Conservation Laws / Randall J. LeVeque / Bâle (CHE) ; Boston, MA : Birkhäuser (1992)
PermalinkOptimal Stopping and Free-Boundary Problems / Goran Peskir / Bâle (CHE) ; Boston, MA : Birkhäuser (2006)
PermalinkSelected Chapters in the Calculus of Variations / Jürgen K. Moser / Bâle (CHE) ; Boston, MA : Birkhäuser (2003)
PermalinkSome Aspects of Brownian Motion / Marc Yor / Bâle (CHE) ; Boston, MA : Birkhäuser (1997)
PermalinkSpatial branching processes random snackes and partial differential equations / Jean-François Le Gall / Bâle (CHE) ; Boston, MA : Birkhäuser (1999)
PermalinkSpatial Branching Processes, Random Snakes and Partial Differential Equations / Jean-François Le Gall / Bâle (CHE) ; Boston, MA : Birkhäuser (1999)
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