The prescribed point area estimate for minimal submanifolds in constant curvature

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.

arXiv comment21 pages, 2 figures; v2: moved some discussion on monotonicity to new preprint, other minor changes; comments welcome!