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Lectures on Nonsmooth Differential Geometry, Hardcover by Gigli, Nicola; Pasq...
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eBay item number:403859622201
Item specifics
- Condition
- Book Title
- Lectures on Nonsmooth Differential Geometry
- Subject
- Geometry / Differential, Mathematical Analysis
- ISBN
- 9783030386122
- Subject Area
- Mathematics
- Publication Name
- Lectures on Nonsmooth Differential Geometry
- Item Length
- 9.3 in
- Publisher
- Springer International Publishing A&G
- Publication Year
- 2020
- Series
- Sissa Springer Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Width
- 6.1 in
- Item Weight
- 17.4 Oz
- Number of Pages
- Xi, 204 Pages
About this product
Product Information
This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces - known as RCD spaces - satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of "infinitesimally Hilbertian" metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking acomprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry.
Product Identifiers
Publisher
Springer International Publishing A&G
ISBN-10
3030386120
ISBN-13
9783030386122
eBay Product ID (ePID)
2309642622
Product Key Features
Publication Name
Lectures on Nonsmooth Differential Geometry
Format
Hardcover
Language
English
Subject
Geometry / Differential, Mathematical Analysis
Publication Year
2020
Series
Sissa Springer Ser.
Type
Textbook
Subject Area
Mathematics
Number of Pages
Xi, 204 Pages
Dimensions
Item Length
9.3 in
Item Width
6.1 in
Item Weight
17.4 Oz
Additional Product Features
Series Volume Number
2
Number of Volumes
1 Vol.
Lc Classification Number
Qa641-670
Reviews
"The lecture notes in this book are a gentle introduction to the topic, intended for readers with no prior exposure to non-smooth analysis, and hint towards the most recent developments of the theory. ... This book is written in a clear and accessible way. It is definitely a recommended introduction to a quickly developing subject." (Daniele Semola, Mathematical Reviews, February, 2023) "The book is written in a clear and precise style. The notions are well motivated and many examples are given. In the reviewer's opinion, this monograph will be of great interest to Ph.D. students and researchers working in the field of nonsmooth differential geometry." (Gabriel Eduard Vilcu, zbMATH 1452.53002, 2021), "The book is written in a clear and precise style. The notions are well motivated and many examples are given. In the reviewer's opinion, this monograph will be of great interest to Ph.D. students and researchers working in the field of nonsmooth differential geometry." (Gabriel Eduard Vilcu, zbMATH 1452.53002, 2021)
Table of Content
1. Preliminaries.- 2. Sobolev calculus on metric measure spaces.- 3. The theory of normed modules.- 4. First-order calculus on metric measure spaces.- 5. Heat ow on metric measure spaces.- 6. Second-order calculus on RCD spaces.- 7. Appendix A: Functional analytic tools.- 8. Appendix B: Solutions to the exercises.
Copyright Date
2020
Illustrated
Yes
Item description from the seller
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eBay item number:403859622201
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Granger, Indiana, United States
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