English

The prescribed point area estimate for minimal submanifolds in constant curvature

Differential Geometry 2022-10-10 v2

Abstract

We prove a sharp area estimate for minimal submanifolds that pass through a prescribed point in a geodesic ball in hyperbolic space, in any dimension and codimension. In certain cases, we also prove the corresponding estimate in the sphere. Our estimates are analogous to those of Brendle and Hung in the Euclidean setting.

Keywords

Cite

@article{arxiv.2206.08302,
  title  = {The prescribed point area estimate for minimal submanifolds in constant curvature},
  author = {Keaton Naff and Jonathan J. Zhu},
  journal= {arXiv preprint arXiv:2206.08302},
  year   = {2022}
}

Comments

21 pages, 2 figures; v2: moved some discussion on monotonicity to new preprint, other minor changes; comments welcome!