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...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.展开更多
We study microscopic convexity properties of convex solutions of fully nonlinear parabolic equations under a structural condition introduced by Bian-Guan.We prove weak Harnack inequalities for the eigenvalues of the s...We study microscopic convexity properties of convex solutions of fully nonlinear parabolic equations under a structural condition introduced by Bian-Guan.We prove weak Harnack inequalities for the eigenvalues of the spatial Hessian of solutions and obtain the monotonicity of Hessian’s rank with respect to time.展开更多
基金supported by National Natural Science Foundation of China(Grant No.10871187)
文摘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.
文摘We study microscopic convexity properties of convex solutions of fully nonlinear parabolic equations under a structural condition introduced by Bian-Guan.We prove weak Harnack inequalities for the eigenvalues of the spatial Hessian of solutions and obtain the monotonicity of Hessian’s rank with respect to time.
