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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-…
math.AP2025
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…
math.AP2025
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)}Ï_{\{u<0\}} \; \text{ in } \mathbb{R}^n, \quad \nab…