On Space-Time Quasiconcave Solutions of the Heat Equation
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-3524-0 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-3524-0 (ISBN)
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Presents 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, the authors obtain some results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring.
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.
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.
Chuanqiang Chen, Zhejiang University of Technology, Hangzhou, China. Xinan Ma, University of Science and Technology of China, Hefei, China. Paolo Salani, Universita di Firenze, Italy.
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.
| Erscheinungsdatum | 01.07.2019 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 180 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-3524-1 / 1470435241 |
| ISBN-13 | 978-1-4704-3524-0 / 9781470435240 |
| Zustand | Neuware |
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