The Genus-Decreasing Property of Mean Curvature Flow, I

Brian White

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arXiv · 2601.13787

The Genus-Decreasing Property of Mean Curvature Flow, I

Brian White

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Abstract

This paper proves that, in mean curvature flow of a compact surface in a complete $3$-manifold with Ricci curvature bounded below, the genus of the regular set is a decreasing function of time as long as the only singularities are given by shrinking sphere and shrinking cylinder tangent flows. The paper also proves some local versions of that fact.

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Brian White. 2026-01-20. The Genus-Decreasing Property of Mean Curvature Flow, I. https://arxiv.org/abs/2601.13787

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