Author

Raphael Tsiamis

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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

On Chern's conjecture for minimal submanifolds of the sphere

A well-known conjecture of Chern, do Carmo, and Kobayashi asserts that, for $n,m \geq 1$, the scalar curvature of a closed, minimally immersed $n$-submanifold of $\mathbb{S}^{n+m}$ with second fundamental form of constant length takes values in a discrete set. This property holds in every codimension when $n \in \{1,2\...

B. Firester, Raphael Tsiamis · 5 citations