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