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math.AP2026
Singularity models for the Bernoulli free boundary problem from isoparametric hypersurfaces
Benjy Firester, Raphael Tsiamis, Zihui Zhao
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…
math.AP2026
Regularity of varifolds with bounded anisotropic first variation
Antonio De Rosa, Benjy Firester, Raphael Tsiamis
We prove an -regularity theorem for -varifolds with mean curvature in , , with respect to an anisotropic integrand satisfying a Michael-Simon inequality a…
math.AP2026
Stability inequalities for one-phase cones
Benjy Firester, Raphael Tsiamis, Yipeng Wang
We obtain strict stability inequalities for homogeneous solutions of the one-phase Bernoulli problem. We prove that in dimension and above, cohomogeneity one solutions with bi-…