Comparison Theorems in Riemannian Geometry: How Curvature Affects Topology - Couverture souple

Kröncke, Klaus

 
9783639494419: Comparison Theorems in Riemannian Geometry: How Curvature Affects Topology
Couverture souple
ISBN 10 : 3639494415 ISBN 13 : 9783639494419
Editeur : AV Akademikerverlag, 2014

Synopsis

The main subject of this work are results of global Riemannian geometry. In all of these theorems we assume some local property of the space (usually formulated using curvature assumption) to derive some information about the global structure of the space, including the topological type of the manifold. In the first part of the work, we study the Bonnet-Myers theorem, the Rauch comparison theorem and the Cartan-Hadamard theorem. The second part is devoted to the sphere theorem, which was proven by Berger and Klingenberg. After extensive preparations, we give a complete proof of the theorem. Finally, we briefly discuss some recent developments that build on the sphere theorem.

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Présentation de l'éditeur

The main subject of this work are results of global Riemannian geometry. In all of these theorems we assume some local property of the space (usually formulated using curvature assumption) to derive some information about the global structure of the space, including the topological type of the manifold. In the first part of the work, we study the Bonnet-Myers theorem, the Rauch comparison theorem and the Cartan-Hadamard theorem. The second part is devoted to the sphere theorem, which was proven by Berger and Klingenberg. After extensive preparations, we give a complete proof of the theorem. Finally, we briefly discuss some recent developments that build on the sphere theorem.

Biographie de l'auteur

The author was born in 1986 in Vienna. After finishing school in June 2004, he studied Mathematics, Physics and Geography at the University of Vienna. After receiving his Diploma in Mathematics in September 2010, he moved to Potsdam for his doctorate. He finshed his doctorate studies in December 2013.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
AV Akademikerverlag
Date d'édition
2014
Langue
anglais
ISBN 10 
3639494415
ISBN 13 
9783639494419
Reliure
Broché
Nombre de pages
96
Coordonnées du fabricant
non disponible
Personne responsable
non disponible