Arizmendi Echegaray / Hernández-Lamoneda / Herrera Guzmán Recent Advances in Alexandrov Geometry

1. Auflage 2022
ISBN: 978-3-030-99298-9
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 111 Seiten, eBook

Reihe: 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-Garci´a’s minicourse was completed in collaboration with Jesu´s Nun~ez-Zimbro´n. 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.Jesu´s Nun~ez-Zimbro´n’s contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.

Zielgruppe

Research

Autoren/Hrsg.

Arizmendi Echegaray, Gerardo

Hernández-Lamoneda, Luis

Herrera Guzmán, Rafael

Inhaltsverzeichnis

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

Leseproben

ez-Zimbro´n. 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.Jesu´s Nun