2023/07/11 by Jia-Yong Wu, Wu, Jia-Yong
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2307.04983
openalex publication_date 2023/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.