"Geometria analítica." . . "Geometria analítica" . "Riemannsche Mannigfaltigkeit." . . "Géométrie analytique." . . "Geometrie diferenţială." . . "Theoretical, Mathematical and Computational Physics" . . "Theoretical, Mathematical and Computational Physics." . "espace symétrique." . . "Riemann, Geometría de." . . "Geometry, Differential." . . "Geometry, Riemannian." . . "geometry - riemannian" . "Geometry, Riemannian" . "SpringerLink (Service en ligne)" . . "Differential Geometry." . . "Connexions (mathématiques)." . . "Física matemàtica." . . "Electronic books." . . "Exercice géométrie différentielle." . . "Geometria diferencial." . . "Riemann-geometria." . . "variété riemannienne." . . "Globale analyse." . . "géodésie." . . "théorie Morse." . . "Riemannsche Geometrie 0 Gesamtdarstellung." . . "Géométrie différentielle globale." . . "Geometrie Riemann." . . "Riemann, Variétés de." . . "Matematică." . . "Matemàtica." . "Géodésiques (mathématiques)." . . "Géométrie de Riemann." . . "Geometri, Riemannian." . . "Physique mathématique." . . "Champs, Théorie quantique des." . . "Teoria quàntica de camps." . . "Courbure." . . "homologie Floer." . . "ANÁLISE GLOBAL." . . "Fizică matematică." . . "géométrie différentielle." . . "Géométrie différentielle." . "Morse, Théorie de." . . "Mathematics." . . "cohomologie De Rham." . . "Cohomologie de Rham." . "Geometrische Analysis." . . "Geometrische Analysis" . "Systems theory." . . "Géodésique fermée." . . "Applications harmoniques." . . . . . "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 . "Riemannian Geometry and Geometric Analysis"@en . "Riemannian Geometry and Geometric Analysis" . "Lehrbuch" . . . . . . . "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." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Llibres electrònics" . . . . . . . . . . . "Online-Publikation" . . . . . . . . . "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." . "Electronic books"@en . "Electronic books" . . . . . . . . . . . . . . "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." . . . . . . . . . "Riemannian geometry and geometric analysis"@en . "Riemannian geometry and geometric analysis" . . . . . . . . . . . . . . "Geometria de Riemann." . . "Geometria de Riemann" . "Geometŕia de Riemann" . "Geometría de Riemann." . "Équations différentielles elliptiques." . . "Riemannscher Raum." . . "Geometria Riemanna." . . "Riemannsche Geometrie." . . "Riemannsche Geometrie" . "Riemann-vlakken." . . "Riemann, Géométrie de." . . "Riemann, géométrie de." . "Mathematical physics." . . "Differentiaalmeetkunde." . . "GEOMETRIA RIEMANNIANA." . . "Geometria riemanniana." . "Geometría riemanniana." . "Riemannsche Geometrie Lehrbuch." . . . . "Global differential geometry." . . "géométrie riemannienne." . . "Geometria Riemanna podręczniki akademickie." . . "forme différentielle." . . "Mathematical and Computational Physics." . . "Mathematical and Computational Physics" . "Geometrie diferenţială globală." . .