On space-time quasiconcave solutions of the heat equation /

"In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly convexity results of the spatial and space-time level...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Chen, Chuanqiang (Author), Ma, Xinan (Author), Salani, Paolo (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence, RI : American Mathematical Society, [2019]
Series:Memoirs of the American Mathematical Society ; no. 1244.
Subjects:
Heat equation.
Convex domains.
Space and time.
Équation de la chaleur.
Algèbres convexes.
Funciones convexas
Espacio y tiempo
Convex domains
Heat equation
Space and time
Online Access:Texto completo
Table of Contents:
  • Cover; Title page; Chapter 1. \040Introduction; Chapter 2. Basic definitions and the Constant Rank Theorem technique; 2.1. Preliminaries; 2.2. A constant rank theorem for the space-time convex solution of the heat equation; 2.3. The strict convexity of the level sets of harmonic functions in convex rings; Chapter 3. A microscopic space-time Convexity Principle for space-time level sets; 3.1. A constant rank theorem for the spatial second fundamental form; 3.2. A constant rank theorem for the space-time second fundamental form: CASE 1
  • 3.3. A constant rank theorem for the space-time second fundamental form: CASE 2Chapter 4. The Strict Convexity of Space-time Level Sets; 4.1. The strict convexity of space-time level sets of Borell's solution; 4.2. Proof of Theorem 1.0.3; Chapter 5. Appendix: the proof in dimension =2; 5.1. minimal rank =0; 5.2. minimal rank =1; Bibliography; Back Cover

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