An inequality for length and volume in the complex projective plane
Differential Geometry
2020-09-09 v2 Analysis of PDEs
Geometric Topology
Abstract
We prove a new inequality relating volume to length of closed geodesics on area minimizers for generic metrics on the complex projective plane. We exploit recent regularity results for area minimizers by Moore and White, and the Kronheimer--Mrowka proof of the Thom conjecture.
Cite
@article{arxiv.2001.00157,
title = {An inequality for length and volume in the complex projective plane},
author = {Mikhail G. Katz},
journal= {arXiv preprint arXiv:2001.00157},
year = {2020}
}
Comments
10 pages; to appear in Geometriae Dedicata