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Mean curvature flow via convex functions on Grassmannian manifolds
Y. L. Xin, Ling Yang
Using the convex functions in Grassmannian manifolds we can carry out interior estimates for mean curvature flow of higher codimension. In this way some of the results of Ecker-Hui…
Convex functions on Grassmannian manifolds and Lawson-Osserman problem
Y. L. Xin, Ling Yang
We derive estimates of the Hessian of two smooth functions defined on Grassmannian manifold. Based on it, we can derive curvature estimates for minimal submanifolds in Euclidean sp…
Curvature estimates for minimal submanifolds of higher codimension
Y. L. Xin, Ling Yang
We derive curvature estimates for minimal submanifolds in Euclidean space for arbitrary dimension and codimension via Gauss map. Thus, Schoen-Simon-Yau's results and Ecker-Huisken'…
Some aspects of the global geometry of entire space-like submanifolds
Juergen Jost, Yuan-Long Xin
We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global…