Locally constrained inverse curvature flow and Alexandrov-Fenchel type inequalities in de Sitter space

TL;DR

This paper investigates a specific inverse curvature flow in de Sitter space, deriving Alexandrov-Fenchel inequalities under certain geometric conditions, contributing to the understanding of spacelike hypersurfaces in this setting.

Contribution

It introduces a new locally constrained inverse curvature flow in de Sitter space and establishes Alexandrov-Fenchel inequalities assuming a Heintze-Karcher inequality.

Findings

Derivation of Alexandrov-Fenchel inequalities in de Sitter space

Analysis of the behavior of the inverse curvature flow

Conditions under which inequalities hold

Abstract

In this paper, we study the behavior of some locally constrained inverse curvature flow in de Sitter space, with initial value any closed spacelike $k$-convex hypersurface satisfying some pinching condition. Assume further the Heintze-Karcher inequality for any closed spacelike mean convex hypersurface in de Sitter space, we derive a class of Alexandrov-Fenchel inequalities.