WorldCat Identities

Ballmann, Werner

Overview
Works: 41 works in 116 publications in 4 languages and 1,444 library holdings
Roles: Author, Editor, Thesis advisor
Classifications: QA649, 516.36
Publication Timeline
.
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 self-contained 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 265 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 Hadamard-Cartan 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 self-contained 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 non-specialist. 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 )

13 editions published in 2006 in English and held by 213 WorldCat member libraries worldwide

These notes are based on lectures the author held at the University of Bonn and the Erwin-Schrödinger-Institute 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 Chern-Weil theory, symmetric spaces, and L2-cohomology
Einführung in die Geometrie und Topologie by Werner Ballmann( )

7 editions published in 2015 in German and held by 70 WorldCat member libraries worldwide

Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet
Der Satz von Lusternik und Schnirelmann by Werner Ballmann( Book )

7 editions published in 1978 in 3 languages and held by 67 WorldCat member libraries worldwide

Arbeitstagung Bonn 2013 : in memory of Friedrich Hirzebruch by Werner Ballmann( Book )

9 editions published in 2016 in English and held by 43 WorldCat member libraries worldwide

This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung. (4e de couv.)
Der Hafen Oldenburg : Entwicklung und Struktur, Bedeutung und Verflechtung by Werner Ballmann( Book )

7 editions published in 1976 in German and held by 40 WorldCat member libraries worldwide

Beitrag zur Klärung des betriebswirtschaftlichen Investitionsbegriffes und zur Entwicklung einer Investitionspolitik der Unternehmung by Werner Ballmann( Book )

3 editions published in 1954 in German and held by 27 WorldCat member libraries worldwide

Einige neue Resultate über Mannigfaltigkeiten nicht positiver Krümmung by Werner Ballmann( Book )

1 edition published in 1978 in German and held by 7 WorldCat member libraries worldwide

Crystalline Dieudonné module theory via formal and rigid geometry by A. J. de Jong( Book )

1 edition published in 1996 in French and held by 5 WorldCat member libraries worldwide

An estimate for the measure theoretic entropy of geodesic flows by Werner Ballmann( Book )

2 editions published in 1987 in German and English and held by 4 WorldCat member libraries worldwide

Differentialgeometrie im Großen : 08.06. - 14.06.1997( Book )

2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide

The Martin boundary of certain Hadamard manifolds by Werner Ballmann( Book )

2 editions published in 1990 in German and English and held by 4 WorldCat member libraries worldwide

Differentialgeometrie im Großen : June 10th - June 16th, 2001( Book )

1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide

Geometric rigidity and hyperbolic dynamics : 18. February - 24. February, 2001( Book )

1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide

Manifolds of Nonpositive Curvature by Werner Ballmann( )

1 edition published in 1985 in English and held by 3 WorldCat member libraries worldwide

Méthodes spinorielles et géométrie para-complexe et para-quaternionique en théorie des sous-variétés by Marie-Amélie Paillusseau-Lawn( Book )

1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide

This thesis is devoted to the theory of immersions, using methods of spin geometry, para-complex and para-quaternionic geometry. It is subdivided into three different topics. The first two are related to the study of conformal immersions of pseudo-Riemannian surfaces. On the one hand we study the immersion into three-dimensional pseudo-Euclidean spaces: with the methods of para-complex geometry and using real spinor representations, we prove the equivalence between the data of a conformal immersion of a Lorentzian surface in R2,1 and spinors satisfying a Dirac-type equation. On the other hand, we consider immersions of such surfaces into the four-dimensional pseudo-sphere S2,2: a one-to-one correspondence between such immersions and para-quaternionic line subbundles of the trivial bundle M X H2 is given. Considering a particular (para-)complex structure on this bundle, namely the mean curvature pseudo-sphere congruence, and the para-quaternionic Hopf fields of the immersion, we define the Willmore functional of the surface and can express its energy as the sum of this functional and of a topological invariant. The last topic is more general and deals with para-complex vector bundles and para-complex affine immersions. We introduce para-holomorphic vector bundles and characterize para-holomorphic subbundles and subbundles of type (1,1) in terms of the associated induced connections and second fundamental forms. The fundamental equations for general decompositions of vector bundles with connection are studied in the case where some of the (sub)bundle are para-holomorphic in order to prove existence and uniqueness theorems of para-complex affine immersions
Beitrag zur Klärung des betriebwirtschaftlichen Investitionsbegriffes und zur Entwicklung einer Investitionspolitik der Unternehmung by Werner Ballmann( Book )

1 edition published in 1954 in German and held by 2 WorldCat member libraries worldwide

Boundary value problems for elliptic differential operators of first order by Christian Bär( )

1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide

We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncom- pact, but the boundary is assumed to be compact.We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regurality of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson’s relative index theorem and a generalization of the cobordism theorem
Géométrie tt* et applications pluriharmoniques by Lars Schäfer( Book )

1 edition published in 2006 in French and held by 1 WorldCat member library worldwide

In this work we introduce the real differential geometric notion of a tt*-bundle (E,D,S), a metric tt*-bundle (E,D,S,g) and a symplectic tt*-bundle (E,D,S,omega) on an abstract vector bundle E over an almost complex manifold (M,J). With this notion we construct, generalizing Dubrovin, a correspondence between metric tt*-bundles over complex manifolds (M,J) and admissible pluriharmonic maps from (M,J) into the pseudo-Riemannian symmetric space GL(r,R)/O(p,q) where (p,q) is the signature of the metric g. Moreover, we show a rigidity result for tt*-bundles over compact Kähler manifolds and we obtain as application a special case of Lu's theorem. In addition we study solutions of tt*-bundles (TM,D,S) on the tangent bundle TM of (M,J) and characterize an interesting class of these solutions which contains special complex manifolds and flat nearly Kähler manifolds. We analyze which elements of this class admit metric or symplectic tt*-bundles. Further we consider solutions coming from varitations of Hodge structures (VHS) and harmonic bundles. Applying our correspondence to harmonic bundles we generalize a correspondence given by Simpson. Analyzing the associated pluriharmonic maps we obtain roughly speaking for special Kähler manifolds the dual Gauss map and for VHS of odd weight the period map. In the case of non-integrable complex structures, we need to generalize the notions of pluriharmonic maps and some results. Apart from the rigidity result we generalize all above results to para-complex geometry
 
moreShow More Titles
fewerShow Fewer Titles
Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.74 (from 0.60 for Arbeitstag ... to 0.97 for Beitrag zu ...)

Lectures on spaces of nonpositive curvature
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 deutscher Mathematiker

Werner Ballmann tysk matematikar

Werner Ballmann tysk matematiker

Балманн, Вернер

Languages
English (62)

German (27)

French (2)

Italian (1)

Covers
Lectures on Kähler manifolds