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

作者：Chen, Chuan Qiang^*; Hu, Bo Wen

来源：Acta Mathematica Sinica-English Series, 2013, 29(4): 651-674.

DOI：10.1007/s10114-012-1495-z

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

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.

• 出版日期2013-4
• 单位中国科学技术大学; 西南科技大学