Equifocal hypersurfaces in symmetric spaces of compact type and backward mean curvature flows

Kurando Baba; Naoyuki Koike

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arXiv · 2607.25025

Equifocal hypersurfaces in symmetric spaces of compact type and backward mean curvature flows

Kurando Baba·Naoyuki Koike

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Abstract

We first derive a formula for the mean curvature and the squared norm of the shape operator of equifocal hypersurfaces in simply-connected irreducible symmetric spaces of compact type. The formulas are given explicitly in terms of the tangential focal data of the equifocal hypersurfaces. Third, we study the backward mean curvature flow for equifocal hypersurfaces. The long-time existence of this flow for an equifocal hypersurface was established by Liu and Radeschi. We analyze the time evolution of the mean curvature and the squared norm of the shape operator along the long-time solution, thereby we generalize the result of Liu and Terng for isoparametric hypersurfaces in the sphere. Our analysis also gives an extension of Liu-Terng conjecture on the backward mean curvature flows in the sphere to the simply-connected irreducible symmetric space of compact type.

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Kurando Baba, Naoyuki Koike. 2026-07-27. Equifocal hypersurfaces in symmetric spaces of compact type and backward mean curvature flows. https://arxiv.org/abs/2607.25025

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