https://neckpinch.com/authors/benjy-firester/New arXiv papers by Benjy Firester, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2508.05551/arxiv:2508.05551Thu, 07 Aug 2025 00:00:00 GMTTristan C. Collins, Benjy Firester — We solve a general class of free boundary Monge-Ampère equations given by det D²u = λ(f(−u))/(g(u^⋆)h(∇u))χ_(u<0\) in ℝⁿ, ∇u (ℝⁿ) = P where P is a bounded convex set containing the origin, and h>0 on P. We consider applications to optimal transport with degenerate densities, Monge-Ampère eigenvalue problems, and geometric problems including a hemispherical Minkowski problem and free boundary Kähler-Ricci solitons on toric Fano manifolds.Gauss curvature flowRicci solitonsKähler–Ricci solitonsKähler geometryLimit spaces & RCDFree boundary & capillaryEigenvalues & spectrum https://neckpinch.com/papers/2408.13982/arxiv:2408.13982Mon, 26 Aug 2024 00:00:00 GMTBenjy Firester, Raphael Tsiamis — We introduce new families of four-dimensional Ricci solitons of cohomogeneity two with volume collapsing ends. In a local presentation of the metric conformal to a product, we reduce the soliton equation to a degenerate Monge-Ampère equation for the conformal factor coupled with ODEs. We obtain explicit complete expanding solitons as well as abstract existence results for shrinking and steady solitons with boundary. These families of Ricci solitons specialize to classical examples of Einstein and soliton metrics. We also classify local solutions of this Monge-Ampère equation to prove rigidity for these solitons.Ricci solitons(Non)collapsing4-manifoldsKähler geometryHomogeneous spacesStability & uniqueness