Vector calculus for tamed dirichlet spaces / Mathias Braun.

Format:

Book

Author/Creator:

Braun, Mathias (Mathias Viktor Joachim), author.

Series:

Memoirs of the American Mathematical Society ; v. 1522.

Memoirs of the American Mathematical Society, 0065-9266 ; v. 1522

Language:

English

Subjects (All):

Calculus.

Dirichlet principle.

calculus.

Physical Description:

viii, 135 pages ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2024

Summary:

In the language of L∞-modules proposed by Gigli, we introduce a first order calculus on a topological Lusin measure space (M, m) carrying a quasi-regular, strongly local Dirichlet form \usefontUBOONDOX-calmnE. Furthermore, we develop a second order calculus if (M, \usefontUBOONDOX-calmnE, m) is tamed by a signed measure in the extended Kato class in the sense of Erbar, Rigoni, Sturm and Tamanini. This allows us to define e.g. Hessians, covariant and exterior derivatives, Ricci curvature, and second fundamental form.

Contents:

List of main vector spaces

Introduction

Chapter 1. First order differential structure

Chapter 2. Second order differential structure

Appendix A. Extrinsic approaches

Bibliography.

Notes:

Includes bibliographical references.

ISBN:

1470471825

9781470471828

OCLC:

1477764024