Diameter estimates for submanifolds in manifolds with nonnegative curvature
Differential Geometry
2026-03-20 v2
Abstract
Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we can estimate its intrinsic diameter in terms of its mean curvature field integral and the length of its boundary. These results are supplements of previous work of Topping, Wu-Zheng and Paeng.
Cite
@article{arxiv.2307.04983,
title = {Diameter estimates for submanifolds in manifolds with nonnegative curvature},
author = {Jia-Yong Wu},
journal= {arXiv preprint arXiv:2307.04983},
year = {2026}
}
Comments
add a comment in Remark 1.2