How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax
  Remote Access

On Space-Time Quasiconcave Solutions of the Heat Equation


About this Title

Chuanqiang Chen, Xinan Ma and Paolo Salani

Publication: Memoirs of the American Mathematical Society
Publication Year: 2019; Volume 259, Number 1244
ISBNs: 978-1-4704-3524-0 (print); 978-1-4704-5243-8 (online)
DOI: https://doi.org/10.1090/memo/1244
Published electronically: April 12, 2019
Keywords:Heat equation, quasiconcavity, space-time level set, constant rank theorem, space-time quasiconcave solution

View full volume PDF

View other years and numbers:

Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Basic definitions and the Constant Rank Theorem technique
  • Chapter 3. A microscopic space-time Convexity Principle for space-time level sets
  • Chapter 4. The Strict Convexity of Space-time Level Sets
  • Chapter 5. Appendix: the proof in dimension $n=2$

Abstract


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 sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain our ideas and for completeness, we 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.

References [Enhancements On Off] (What's this?)