Author

Zihui Zhao

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Preprint Sep 2026

Singularity models for the Bernoulli free boundary problem from isoparametric hypersurfaces

We develop a general construction of homogeneous solutions to the Bernoulli free boundary problem, as well as general extremal domains on the sphere, from isoparametric foliations of the sphere. Our construction produces rich families of infinitely many new examples with sophisticated topologies connected to minimal su...

B. Firester, Raphael Tsiamis, Zi-Hui Zhao · 0 citations

Preprint Aug 2026

Singularity formation and self-shrinkers for the parabolic Bernoulli problem

We study singularity formation for classical solutions of the parabolic Bernoulli free boundary problem and the associated self-similar profiles. Inspired by Ricci and mean curvature flows, we introduce a Type I assumption on the blow-up rate at a singular free boundary point, under which the parabolic rescalings are c...

Hunter Liu, Sebastián Muñoz, Zihui Zhao · 0 citations