On Space-Time Quasiconcave Solutions of the Heat Equation (Memoirs of the American Mathematical Society)

Chen, Chuanqiang/ Ma, Xinan/ Salani, Paolo

American Mathematical Society（2020/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 83 p.
• 言語 ENG
• 商品コード 9781470435240
• DDC分類 515.353

Full Description

In this paper the authors 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, they obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain their ideas and for completeness, the authors also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function.

Contents

Introduction
Basic definitions and the constant rank theorem technique
A microscopic space-time convexity principle for space-time level sets
The strict convexity of space-time level sets
Appendix: the proof in dimension $n=2$
Bibliography.