A locally constrained inverse Hessian quotient flow in de Sitter space

Kuicheng Ma

A locally constrained inverse Hessian quotient flow in de Sitter space

Differential Geometry 2025-12-19 v2

Authors: Kuicheng Ma

Abstract

In this paper, an Alexandrov-Fenchel inequality is established for closed $2$ -convex spacelike hypersurface in de Sitter space by investigating the behavior of the locally constrained inverse curvature flow \begin{align} \frac{\partial }{\partial t}x=\bigg(u-\frac{\lambda'E_1}{E_2}\bigg)\nu,\nonumber \end{align} which provides a partial answer to the conjecture raised by Hu and Li in \cite{HL}.

Keywords

inverse Hessian flow de Sitter space Alexandrov-Fenchel inequality 2-convex hypersurface curvature flow

Cite

@article{arxiv.2507.11149,
  title  = {A locally constrained inverse Hessian quotient flow in de Sitter space},
  author = {Kuicheng Ma},
  journal= {arXiv preprint arXiv:2507.11149},
  year   = {2025}
}

Comments

I realized that there is a serious mistake in Section 4 (on page 9) . More precisely, the uniform upper bound for $E_1$ is unavailable with my argument

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