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