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Riemannian Geometry and Geometric Analysis

From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry,e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. It is a good introduction to Riemannian geometry. The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references." Math. Reviews. The second edition contains a new chapter on variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. These topics are carefully and systematically developed, and the new edition contains a thorough treatment of the relevant background material, namely spin geometry and Dirac operators. The new material is based on a course "Geometry and Physics" at the University of Leipzig that was attented by graduate students, postdocs and researchers from other areas of mathematics. Much of the material is included here for the first time in a textbook, and the book will lead the reader to some of the hottest topics of contemporary mathematical research.

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  • "From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry,e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. It is a good introduction to Riemannian geometry. The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references." Math. Reviews. The second edition contains a new chapter on variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. These topics are carefully and systematically developed, and the new edition contains a thorough treatment of the relevant background material, namely spin geometry and Dirac operators. The new material is based on a course "Geometry and Physics" at the University of Leipzig that was attented by graduate students, postdocs and researchers from other areas of mathematics. Much of the material is included here for the first time in a textbook, and the book will lead the reader to some of the hottest topics of contemporary mathematical research."@en
  • "Offering some topics of contemporary mathematical research, this fourth edition provides an introduction to Riemannian geometry and geometric analysis. It focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, and the existence of harmonic mappings. It also includes an introduction to Kahler geometry."@en
  • "Offering some of the topics of contemporary mathematical research, this fourth edition includes a systematic introduction to Kahler geometry and the presentation of additional techniques from geometric analysis."@en
  • "This is a textbook for Riemannian Geometry and Geometric Analysis, introducing techniques from nonlinear analysis at an early stage. Such techniques have recently become an indispensable tool in research in geometry and they are treated in a textbook for the first time. Subjects treated are: Differentiable and Riemannian manifolds, metric properties, tensor calculus, vector bundles, the Hodge theorem for de Rham cohomology, connections and curvature, the Yang-Mills functional, geodesics and Jacobi fields, Rauch comparison theorem and applications, Morse theory (including an introduction to algebraic topology), applications to the existence of closed geodesics, symmetric spaces and Kahler manifolds, the Palais-Smale condition and closed geodesics, harmonic maps, definition and basic properties, existence and uniqueness theorems, applications, minimal surfaces, regularity results. In an appendix Sobolev spaces and regularity theory for linear elliptic equations are discussed in detail."
  • "This textbook introduces techniques from nonlinear analysis at an early stage. Such techniques have recently become an indispensable tool in research in geometry, and they are treated here for the first time in a textbook. Topics treated include: Differentiable and Riemannian manifolds, metric properties, tensor calculus, vector bundles; the Hodge Theorem for de Rham cohomology; connections and curvature, the Yang-Mills functional; geodesics and Jacobi fields, Rauch comparison theorem and applications; Morse theory (including an introduction to algebraic topology), applications to the existence of closed geodesics; symmetric spaces and Kähler manifolds; the Palais-Smale condition and closed geodesics; Harmonic maps, minimal surfaces."
  • "The second edition featured a new chapter with a systematic development of variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. This third edition gives a new presentation of Morse theory and Floer homology that emphasises the geometric aspects and integrates it into the context of Riemannian geometry and geometric analysis. It also gives a new presentation of the geometric aspects of harmonic maps: This uses geometric methods from the theory of geometric spaces of nonpositive curvature and, at the same time, sheds light on these, as an excellent example of the integration of deep geometric insights and powerful analytical tools. These new materials are based on a course at the University of Leipzig, entitled Geometry and Physics, attended by graduate students, postdocs and researchers from other areas of mathematics. Much of this material appears for the first time in a textbook."

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  • "Lehrbuch"
  • "Llibres electrònics"
  • "Online-Publikation"
  • "Electronic books"
  • "Electronic books"@en

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  • "Riemannian Geometry and Geometric Analysis"
  • "Riemannian Geometry and Geometric Analysis"@en
  • "Riemannian geometry and geometric analysis"
  • "Riemannian geometry and geometric analysis"@en

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