New Trends on Analysis and Geometry in Metric Spaces

Levico Terme, Italy 2017

Luigi Ambrosio, Bruno Franchi, Irina Markina , Francesco Serra Cassano

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English

Springer Nature Switzerland AG
05 February 2022

Groups & group theory; Functional analysis & transforms; Integral calculus & equations; Differential & Riemannian geometry; Optimisation

Series: C.I.M.E. Foundation Subseries

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on ""Analysis and Geometry in Metric Spaces"" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.

By: Fabrice Baudoin
Edited by: Luigi Ambrosio, Bruno Franchi, Irina Markina, Francesco Serra Cassano
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 2296
Dimensions: Height: 235mm, Width: 155mm,
Weight: 486g
ISBN: 9783030841409
ISBN 10: 3030841405
Series: C.I.M.E. Foundation Subseries
Pages: 308
Publication Date: 05 February 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

- Introduction to the Notes of the School on Analysis and Geometry in Metric Spaces. - Geometric Inequalities on Riemannian and Sub-Riemannian Manifolds by Heat Semigroups Techniques. - Differentiation of Measures in Metric Spaces. - Sobolev Spaces in Extended Metric-Measure Spaces. - Brief Survey on Functions of Bounded Variation (BV) in Metric Setting.