Convex functions on Grassmannian manifolds and Lawson-Osserman problem
Y. L. Xin, Ling Yang
TL;DR
This paper develops Hessian estimates for functions on Grassmannian manifolds to improve curvature bounds for minimal submanifolds in Euclidean space, enhancing Bernstein-type theorems.
Contribution
It introduces new Hessian estimates on Grassmannians that lead to sharper curvature bounds for minimal submanifolds, advancing Bernstein-type results.
Findings
Improved curvature estimates for minimal submanifolds.
Enhanced Bernstein-type theorems.
New Hessian bounds on Grassmannian manifolds.
Abstract
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 space via Gauss map. In this way, the result for Bernstein type theorem done by Jost and the first author could be improved.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds