Affiliation:
1. Center of Mathematical Sciences Zhejiang University Hangzhou China
2. College of Mathematics and Computer Science Zhejiang Agriculture and Forestry University Hangzhou China
Abstract
AbstractIn this paper, we investigate the rigidity and vanishing properties of compact submanifolds with free boundary of arbitrary codimension in the unit ball. We first show that a minimal submanifold with free boundary in the unit ball satisfying a pointwise or integral curvature pinching condition on the second fundamental form is a flat equatorial disk. Then we prove a vanishing theorem for cohomology groups for submanifolds with free boundary in the unit ball under an integral curvature pinching condition on the trace‐free second fundamental form.
Funder
National Natural Science Foundation of China