Acta Mathematica Sinica, English Series

, Volume 29, Issue 4, pp 651–674

A microscopic convexity principle for spacetime convex solutions of fully nonlinear parabolic equations

Article

DOI: 10.1007/s10114-012-1495-z

Cite this article as:
Chen, C.Q. & Hu, B.W. Acta. Math. Sin.-English Ser. (2013) 29: 651. doi:10.1007/s10114-012-1495-z
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Abstract

We study microscopic spacetime convexity properties of fully nonlinear parabolic partial differential equations. Under certain general structure condition, we establish a constant rank theorem for the spacetime convex solutions of fully nonlinear parabolic equations. At last, we consider the parabolic convexity of solutions to parabolic equations and the convexity of the spacetime second fundamental form of geometric flows.

Keywords

Spacetime convexitymicroscopic convexity principleconstant rank theoremparabolic convexityspacetime second fundamental form

MR(2010) Subject Classification

35K1035B99

Supplementary material

10114_2012_1495_MOESM1_ESM.tex (80 kb)
Supplementary material, approximately 80.1 KB.

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiP. R. China
  2. 2.Department of Mathematics and Applied MathematicsSouthwest University of Science and TechnologyMianyangP. R. China