Ballmann, Werner
Overview
Works:  54 works in 164 publications in 4 languages and 1,366 library holdings 

Roles:  Author, Editor, Contributor 
Classifications:  QA649, 516.36 
Publication Timeline
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Most widely held works by
Werner Ballmann
Manifolds of nonpositive curvature by
Werner Ballmann(
Book
)
18 editions published between 1985 and 2013 in 3 languages and held by 350 WorldCat member libraries worldwide
This volume presents a complete and selfcontained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collge de France in Paris. Among others these lectures threat local and global rigidity problems (e.g., a generalization of the famous Mostow rigidity theorem) and finiteness results for manifolds of finite volume. V. Schroeder wrote up these lectures, including complete and detailed proofs. A lot of background material is added to the first lectures. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank
18 editions published between 1985 and 2013 in 3 languages and held by 350 WorldCat member libraries worldwide
This volume presents a complete and selfcontained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collge de France in Paris. Among others these lectures threat local and global rigidity problems (e.g., a generalization of the famous Mostow rigidity theorem) and finiteness results for manifolds of finite volume. V. Schroeder wrote up these lectures, including complete and detailed proofs. A lot of background material is added to the first lectures. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank
Lectures on spaces of nonpositive curvature by
Werner Ballmann(
Book
)
16 editions published in 1995 in 3 languages and held by 262 WorldCat member libraries worldwide
Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the HadamardCartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a selfcontained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the nonspecialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory
16 editions published in 1995 in 3 languages and held by 262 WorldCat member libraries worldwide
Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the HadamardCartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a selfcontained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the nonspecialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory
Lectures on Kähler manifolds by
Werner Ballmann(
Book
)
12 editions published in 2006 in English and held by 207 WorldCat member libraries worldwide
These notes are based on lectures the author held at the University of Bonn and the ErwinSchrödingerInstitute in Vienna. The aim is to give a thorough introduction to the theory of Kähler manifolds with special emphasis on the differential geometric side of Kähler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kähler manifolds. The more advanced topics are the cohomology of Kähler manifolds, Calabi conjecture, Gromov's Kähler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on ChernWeil theory, symmetric spaces, and L2cohomology
12 editions published in 2006 in English and held by 207 WorldCat member libraries worldwide
These notes are based on lectures the author held at the University of Bonn and the ErwinSchrödingerInstitute in Vienna. The aim is to give a thorough introduction to the theory of Kähler manifolds with special emphasis on the differential geometric side of Kähler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kähler manifolds. The more advanced topics are the cohomology of Kähler manifolds, Calabi conjecture, Gromov's Kähler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on ChernWeil theory, symmetric spaces, and L2cohomology
Einige neue Resultate über Mannigfaltigkeiten nicht positiver Krümmung by
Werner Ballmann(
Book
)
10 editions published between 1978 and 1979 in German and Undetermined and held by 68 WorldCat member libraries worldwide
10 editions published between 1978 and 1979 in German and Undetermined and held by 68 WorldCat member libraries worldwide
Der Satz von Lusternik und Schnirelmann by
Werner Ballmann(
Book
)
6 editions published in 1978 in 3 languages and held by 66 WorldCat member libraries worldwide
6 editions published in 1978 in 3 languages and held by 66 WorldCat member libraries worldwide
Der Hafen Oldenburg : Entwicklung und Struktur, Bedeutung und Verflechtung by
Werner Ballmann(
Book
)
9 editions published between 1976 and 1978 in German and held by 41 WorldCat member libraries worldwide
9 editions published between 1976 and 1978 in German and held by 41 WorldCat member libraries worldwide
Einführung in die Geometrie und Topologie by
Werner Ballmann(
Book
)
5 editions published in 2015 in German and held by 35 WorldCat member libraries worldwide
5 editions published in 2015 in German and held by 35 WorldCat member libraries worldwide
Einführung in die Geometrie und Topologie by
Werner Ballmann(
)
1 edition published in 2015 in German and held by 32 WorldCat member libraries worldwide
1 edition published in 2015 in German and held by 32 WorldCat member libraries worldwide
Beitrag zur Klärung des betriebswirtschaftlichen Investitionsbegriffes und zur Entwicklung einer Investitionspolitik der
Unternehmung by
Werner Ballmann(
Book
)
4 editions published in 1954 in German and held by 29 WorldCat member libraries worldwide
4 editions published in 1954 in German and held by 29 WorldCat member libraries worldwide
Wirtschaftlichkeit des Massentransports bei Zug und Bandförderung im Abraumbetrieb der Braunkohlentagebaue by
Werner Ballmann(
Book
)
4 editions published between 1961 and 1963 in German and held by 23 WorldCat member libraries worldwide
4 editions published between 1961 and 1963 in German and held by 23 WorldCat member libraries worldwide
On the spectral theory of surfaces with cusps by
Werner Ballmann(
Book
)
5 editions published in 1999 in English and held by 11 WorldCat member libraries worldwide
5 editions published in 1999 in English and held by 11 WorldCat member libraries worldwide
Beiträge zur Differentialgeometrie by
Werner Ballmann(
Book
)
5 editions published in 1978 in German and Undetermined and held by 9 WorldCat member libraries worldwide
5 editions published in 1978 in German and Undetermined and held by 9 WorldCat member libraries worldwide
On the spectral theory of manifolds with cusps by
Werner Ballmann(
Book
)
5 editions published in 2000 in English and held by 8 WorldCat member libraries worldwide
5 editions published in 2000 in English and held by 8 WorldCat member libraries worldwide
Amenable isometry groups of Hadamard spaces by
Scot Adams(
Book
)
4 editions published in 1997 in English and held by 7 WorldCat member libraries worldwide
4 editions published in 1997 in English and held by 7 WorldCat member libraries worldwide
Diameter rigidity of spherical polyhedra by
Werner Ballmann(
Book
)
3 editions published in 1996 in English and German and held by 7 WorldCat member libraries worldwide
3 editions published in 1996 in English and German and held by 7 WorldCat member libraries worldwide
Orbihedra of nonpositive curvature by
Werner Ballmann(
Book
)
4 editions published in 1994 in English and German and held by 7 WorldCat member libraries worldwide
4 editions published in 1994 in English and German and held by 7 WorldCat member libraries worldwide
On groups acting on nonpositively curved cubical complexes by
Werner Ballmann(
Book
)
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Nonpositively curved metrics on 2polyhedra by
Werner Ballmann(
Book
)
4 editions published in 1994 in English and German and held by 6 WorldCat member libraries worldwide
4 editions published in 1994 in English and German and held by 6 WorldCat member libraries worldwide
Discretization of positive harmonic functions on Riemannian manifolds and Martin boundary by
Werner Ballmann(
Book
)
3 editions published in 1992 in English and German and held by 6 WorldCat member libraries worldwide
3 editions published in 1992 in English and German and held by 6 WorldCat member libraries worldwide
Crystalline Dieudonné module theory via formal and rigid geometry by
Arthur J De Jong(
Book
)
1 edition published in 1996 in French and held by 5 WorldCat member libraries worldwide
1 edition published in 1996 in French and held by 5 WorldCat member libraries worldwide
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Related Identities
 Schroeder, Viktor
 Gromov, Mikhael 1943
 Brin, Misha Other Writer of accompanying material
 Matthias, HansHeinrich Contributor
 Brin, Michael 1948
 Brüning, Jochen
 Ledrappier, François
 Swiatkowski, Jacek
 European Mathematical Society Publisher
 Schwartz, Richard Evan
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Associated Subjects
Algebraic topology Cell aggregationMathematics Curvature Curves, Algebraic Discrete groups Flows (Differentiable dynamical systems) Geodesic flows Geometry Geometry, Algebraic Geometry, Differential GermanyGronau (North RhineWestphalia) GermanyOldenburg Global analysis (Mathematics) Global differential geometry Group theory Homology theory Homomorphisms (Mathematics) Isometrics (Mathematics) Kählerian manifolds Lattice theory Manifolds (Mathematics) Mathematics Metric spaces Riemannian manifolds Semisimple Lie groups Topological groups Topological transformation groups Topology
Alternative Names
Ballmann, Hans Werner 1951
Ballmann, W. 1951
Ballmann, Werner
Hans Werner Ballmann Duits wiskundige
Hans Werner Ballmann German mathematician
Hans Werner Ballmann mathématicien allemand
Werner Ballmann tysk matematikar
Werner Ballmann tysk matematiker
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