Locally constrained flows and geometric inequalities in sphere
Differential Geometry
2024-04-09 v2 Analysis of PDEs
Abstract
In this paper, we uncover an intriguing algebra property of an element symmetric polynomial. By this property, we establish the longtime existence and convergence of a locally constrained flow, thereby some families of geometric inequalities in sphere can be derived. Meanwhile, a new family of ``three terms'' geometric inequalities involving two weighted curvature integrals and one quermassintegral are proved. Unlike hyperbolic spaces, we also obtain an inverse weighted geometric inequality in sphere.
Keywords
Cite
@article{arxiv.2403.07281,
title = {Locally constrained flows and geometric inequalities in sphere},
author = {Shanwei Ding and Guanghan Li},
journal= {arXiv preprint arXiv:2403.07281},
year = {2024}
}
Comments
There are some errors in the case of hyperbolic space in v1. We removed the corresponding part, and added a locally constrained flow in sphere