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arXiv · 2604.13324

Dimension Bound of Singular Set of One-Phase Free Boundary Problems in Spaces with Two-Sided Ricci Bound

Kai-Hsiang Wang
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Abstract

In this article, we show that for one-phase free boundary problems in noncollapsed limits of $n$-dimensional manifolds with two-sided Ricci curvature bounds, the Hausdorff dimension of the singular set of the free boundary can be bounded by $n-5$, which is sharp in this context.

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Kai-Hsiang Wang. 2026-04-14. Dimension Bound of Singular Set of One-Phase Free Boundary Problems in Spaces with Two-Sided Ricci Bound. https://arxiv.org/abs/2604.13324

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