Recent Advances in Alexandrov Geometry

Gerardo Arizmendi Echegaray, Luis Hernández-Lamoneda, Rafael Herrera Guzmán

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English

Springer Nature Switzerland AG
28 October 2022

Differential & Riemannian geometry; Topology

Series: CIMAT Lectures in Mathematical Sciences

This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT.

Peter Petersen’s part aims at presenting various rigidity results about Alexandrov spaces in a way that facilitates the understanding by a larger audience of geometers of some of the current research in the subject. They contain a brief overview of the fundamental aspects of the theory of Alexandrov spaces with lower curvature bounds, as well as the aforementioned rigidity results with complete proofs.

The text from Fernando Galaz-García’s minicourse was completed in collaboration with Jesús Nuñez-Zimbrón. It presents an up-to-date and panoramic view of the topology and geometry of 3-dimensional Alexandrov spaces, including the classification of positively and non-negatively curved spaces and the geometrization theorem. They also present Lie group actions and their topological and equivariant classifications as well as a brief account of results on collapsing Alexandrov spaces.

Jesús Nuñez-Zimbrón’s contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.

Edited by: Gerardo Arizmendi Echegaray, Luis Hernández-Lamoneda, Rafael Herrera Guzmán
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2022 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 354g
ISBN: 9783030992972
ISBN 10: 3030992977
Series: CIMAT Lectures in Mathematical Sciences
Pages: 111
Publication Date: 28 October 2022
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Rigidity of Alexandrov spaces.- 2. Three-dimensional Alexandrov spaces: a survey.- 3. Topological and geometric rigidity for spaces with curvature bounded below.