1. On Space-Time Quasiconcave Solutions of the Heat Equation
- Author
-
Chuanqiang Chen, Xinan Ma, Paolo Salani, Chuanqiang Chen, Xinan Ma, and Paolo Salani
- Subjects
- Heat equation, Convex domains, Space and time
- Abstract
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.
- Published
- 2019