Existence, Lipschitz regularity, and almost-(N-1)-manifold structure of free boundaries are proved for one-phase Bernoulli problems on non-collapsed RCD(K,N) spaces.
Ding, Minimal hypersurfaces in manifolds of Ricci curvature bounded below , available at arXiv:2109.02483
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One-phase Free Boundary Problems on RCD Metric Measure Spaces
Existence, Lipschitz regularity, and almost-(N-1)-manifold structure of free boundaries are proved for one-phase Bernoulli problems on non-collapsed RCD(K,N) spaces.