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arXiv · 2604.14139

Mean curvature flows with prescribed singular sets

Raphael Tsiamis
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Abstract

For every closed set $K \subset \mathbb{R}^n$ and every $m \geq 2$, we construct a mean-convex ancient solution to mean curvature flow of hypersurfaces in $\mathbb{R}^{m+n}$, with respect to a smooth Riemannian metric arbitrarily $C^\infty$-close to the Euclidean metric, whose first-time singular set is exactly $K \times \{0\}$.

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Raphael Tsiamis. 2026-04-15. Mean curvature flows with prescribed singular sets. https://arxiv.org/abs/2604.14139

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