English

A Systolic Inequality for the Filling Area Conjecture

Differential Geometry 2023-01-23 v1

Abstract

We prove an upper bound on the systolic ratio of an orientable isometric filling of the circle equipped with a Riemannian metric. The bound depends only on the genus of isometric filling. We also apply the bound to the class of orientable isometric filling with a certain lower bound on the systole. We deduce that the Filling Area Conjecture holds true for this class when the genus is sufficiently large.

Keywords

Cite

@article{arxiv.2301.08503,
  title  = {A Systolic Inequality for the Filling Area Conjecture},
  author = {Chaitanya Ambi},
  journal= {arXiv preprint arXiv:2301.08503},
  year   = {2023}
}

Comments

7 pages