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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…
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-…
Homogeneous optimal transport maps between oblique cones
Tristan C. Collins, Benjy Firester, Freid Tong
We construct homogeneous optimal transport maps for the quadratic cost between convex cones with homogeneous, possibly degenerate, densities when the cones satisfy an obliqueness c…
On a general class of free boundary Monge-Ampère equations
Tristan C. Collins, Benjy Firester
We solve a general class of free boundary Monge-Ampère equations given by \[ \det D^2u = λ\dfrac{f(-u)}{g(u^\star)h(\nabla u)}χ_{\{u<0\}} \; \text{ in } \mathbb{R}^n, \quad \nabla…