Gap results for free boundary CMC surfaces in the Euclidean three-ball.
2019
In this note, we prove that if a free boundary constant mean curvature surface $\Sigma$ in an Euclidean 3-ball satisfies a pinching condition on the length of traceless second fundamental tensor, then either $\Sigma$ is a totally umbilical disk or an annulus of revolution. The pinching is sharp since there are portions of some Delaunay surfaces inside the unit Euclidean 3-ball which are free boundary and satisfy the pinching condition.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
13
References
3
Citations
NaN
KQI