https://neckpinch.com/authors/tristan-c-collins/New arXiv papers by Tristan C. Collins, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.24884arxiv:2609.24884Mon, 21 Sep 2026 00:00:00 GMTTristan C. Collins, Genggeng Huang, Freid Tong, Yulun Xu — We prove that a smooth toric Fano fibration admits a complete gradient shrinking Kähler-Ricci soliton.Ricci solitonsKähler–Ricci solitonsKähler geometryAnalytic minimal model program https://arxiv.org/abs/2508.05551arxiv: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://arxiv.org/abs/2405.11049arxiv:2405.11049Fri, 17 May 2024 00:00:00 GMTTristan C. Collins, Adam Jacob, Yu-Shen Lin — We establish a convergence result for the mean curvature flow starting from a totally real submanifold which is "almost minimal" in a precise, quantitative sense. This extends, and makes effective, a result of H. Li for the Lagrangian mean curvature flow.Mean curvature flowLagrangian mean curvature flow