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New Trends on Analysis and Geometry in Metric Spaces

Levico Terme, Italy 2017

  • Conference proceedings
  • © 2022

Overview

Authors:
  1. Fabrice Baudoin

    1. Department of Mathematics, University of Connecticut, Storrs, USA

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  2. Séverine Rigot

    1. Laboratoire de Mathématiques J.A. Dieudonné, Université Côte d'Azur, Nice, France

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  3. Giuseppe Savaré

    1. Department of Decision Sciences, Bocconi University, Milan, Italy

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  4. Nageswari Shanmugalingam

    1. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

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Editors:
  1. Luigi Ambrosio

    1. Scuola Normale Superiore, Pisa, Italy

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  2. Bruno Franchi

    1. Department of Mathematics, University of Bologna, Bologna, Italy

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  3. Irina Markina

    1. Department of Mathematics, University of Bergen, Bergen, Norway

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  4. Francesco Serra Cassano

    1. Department of Mathematics, University of Trento, Trento, Italy

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  • Contains new, original presentations at the forefront of current international research
  • Includes different interconnected subjects with different applications
  • Provides contributions to advanced subjects which offer a useful reference for young researchers

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2296)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (5 papers)

  1. Front Matter

    Pages i-v
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  2. Introduction to the Notes of the School on Analysis and Geometry in Metric Spaces

    • Luigi Ambrosio, Bruno Franchi, Irina Markina, Francesco Serra Cassano
    Pages 1-6

  3. Geometric Inequalities on Riemannian and Sub-Riemannian Manifolds by Heat Semigroups Techniques

    • Fabrice Baudoin
    Pages 7-91

  4. Differentiation of Measures in Metric Spaces

    • Séverine Rigot
    Pages 93-116

  5. Sobolev Spaces in Extended Metric-Measure Spaces

    • Giuseppe Savaré
    Pages 117-276

  6. Brief Survey on Functions of Bounded Variation (BV) in Metric Setting

    • Nageswari Shanmugalingam
    Pages 277-303

  7. Back Matter

    Pages 305-308
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Keywords

About this book

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.

Authors, Editors and Affiliations

  • Scuola Normale Superiore, Pisa, Italy

    Luigi Ambrosio

  • Department of Mathematics, University of Bologna, Bologna, Italy

    Bruno Franchi

  • Department of Mathematics, University of Bergen, Bergen, Norway

    Irina Markina

  • Department of Mathematics, University of Trento, Trento, Italy

    Francesco Serra Cassano

  • Department of Mathematics, University of Connecticut, Storrs, USA

    Fabrice Baudoin

  • Laboratoire de Mathématiques J.A. Dieudonné, Université Côte d'Azur, Nice, France

    Séverine Rigot

  • Department of Decision Sciences, Bocconi University, Milan, Italy

    Giuseppe Savaré

  • Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

    Nageswari Shanmugalingam

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