We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the...We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the principal curvature of the spatial level surfaces.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10871187)supported by the Science Research Program from the Education Department of Heilongjiang Province (Grant No. 11551137)
文摘We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the principal curvature of the spatial level surfaces.