A spherical Bernstein theorem for minimal submanifolds of higher codimension

作者：Jost, J.; Xin, Y. L.; Yang, Ling^*

来源：Calculus of Variations and Partial Differential Equations, 2018, 57(6): 166.

DOI：10.1007/s00526-018-1439-2

• SUB-MANIFOLDS
• RIGIDITY
• GEOMETRY

Combining the tools of geometric analysis with properties of Jordan angles and angle space distributions, we derive a spherical and a Euclidean Bernstein theorem for minimal submanifolds of arbitrary dimension and codimension, under the condition that the Gauss image is contained in some geometrically defined closed region of a Grassmannian manifold. The proof depends on the subharmoncity of an auxiliary function, the Codazzi equations and geometric measure theory.

• 出版日期2018-12
• 单位复旦大学