Moving monotonicity formulae for minimal submanifolds in constant curvature
Differential Geometry
2022-10-10 v1
Abstract
We discover new monotonicity formulae for minimal submanifolds in space forms, which imply the sharp area bound for minimal submanifolds through a prescribed point in a geodesic ball. These monotonicity formulae involve an energy-like integral over sets which are, in general, not geodesic balls. In the Euclidean case, these sets reduce to the moving-centre balls introduced by the second author in [Zhu18].
Cite
@article{arxiv.2210.03263,
title = {Moving monotonicity formulae for minimal submanifolds in constant curvature},
author = {Keaton Naff and Jonathan J. Zhu},
journal= {arXiv preprint arXiv:2210.03263},
year = {2022}
}
Comments
11 pages, 1 figure; comments welcome!