arXiv subjects
Publications and source records attributed to Kuicheng Ma.
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.
In this paper, the long-time existence and convergence results are derived for locally constrained flows with initial value some compact spacelike hypersurface that is suitably pinched in the de Sitter space. As applications, geometric inequalities related to the quermassintegrals as well as the weighted curvature integrals are established.
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}.