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


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


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.


Spacetime convexity microscopic convexity principle constant rank theorem parabolic convexity spacetime second fundamental form 

MR(2010) Subject Classification

35K10 35B99 

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