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Optimal regularity of optimal transport and degenerations of convex cones
Tristan C. Collins, Benjy Firester, Freid Tong
If is an optimal transport map between bounded convex domains and , we characterize the regularity/singularity dichotomy for at $(x,T(x)) \in \partial Ω\times \par…
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…
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…
The anisotropic Michael-Simon inequality
Benjy Firester, Raphael Tsiamis
We prove a Michael-Simon inequality for varifolds of every dimension and codimension with respect to anisotropic energies. In particular, this resolves the problem for every convex…
The anisotropic Michael-Simon inequality for surfaces in every codimension
Benjy Firester, Raphael Tsiamis
We prove a Michael-Simon inequality for -varifolds in , in arbitrary codimension, for anisotropies sufficiently close to the area functional. Building on the ideas…
On Chern's conjecture for minimal submanifolds of the sphere
Benjy Firester, Raphael Tsiamis
A well-known conjecture of Chern, do Carmo, and Kobayashi asserts that, for , the scalar curvature of a closed, minimally immersed -submanifold of …
Topology of minimal surfaces in the sphere from capillarity
Benjy Firester, Raphael Tsiamis
We present a general construction of embedded minimal and constant mean curvature surfaces in and one-phase free boundaries joined by a smooth interpolation by capil…
New minimal surfaces in the sphere from capillary minimal cones
Benjy Firester, Raphael Tsiamis
For every , we construct minimal embeddings of in by doubling the links of free-boundary…
Area-minimizing capillary cones
Benjy Firester, Raphael Tsiamis, Yipeng Wang
We construct non-flat minimal capillary cones with bi-orthogonal symmetry groups for any dimension and contact angle. These cones interpolate between rescalings of a singular solut…
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-…