Locally constrained flows and geometric inequalities in sphere

Autor:	Ding, Shanwei, Li, Guanghan
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.07281 Zobrazit plný text záznamu View this record from Arxiv