https://neckpinch.com/authors/luke-t-peachey/New arXiv papers by Luke T. Peachey, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2509.25081arxiv:2509.25081Mon, 29 Sep 2025 00:00:00 GMTLucas Lavoyer, Luke T. Peachey — We find new examples of steady gradient Ricci solitons with positive curvature operator in dimensions four and above. Utilising a procedure first introduced by Lai, we construct examples with O(p) × O(q) symmetry in dimension p+q for any pair of integers p,q ≥ 2 and discuss their asymptotic geometry.Ricci solitonsSphere theorems https://arxiv.org/abs/2404.12755arxiv:2404.12755Fri, 19 Apr 2024 00:00:00 GMTPak-Yeung Chan, Man-Chun Lee, Luke T. Peachey — Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flow must be an expanding gradient Ricci soliton, and as a consequence, any metric cone at infinity of a complete weakly PIC1 Kähler manifold with Euclidean volume growth is biholomorphic to complex Euclidean space in a canonical way.Ricci flowRicci solitonsSphere theoremsKähler geometryWeak & singular flows https://arxiv.org/abs/2307.05306arxiv:2307.05306Tue, 11 Jul 2023 00:00:00 GMTLuke T. Peachey, Peter M. Topping — The second author and H. Yin have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a nonatomic Radon measure as a volume measure. This led to the discovery of a large array of new expanding Ricci solitons. In this paper we use the recent uniqueness theory in this context, also developed by the second author and H. Yin, to give a complete classification of all expanding Ricci solitons on surfaces. Along the way, we prove a converse to the existence theory that is not constrained to solitons: every complete Ricci flow on a surface over a time interval (0,ε) admits a tdownarrow 0 limit within the class of admissible initial data. This makes surfaces the first nontrivial setting for Ricci flow in which a bijection can be given between the entire set of complete Ricci flows over maximal time intervals (0,T), and a class of initial data that induces them.Ricci flowRicci solitonsSurfacesStability & uniqueness https://arxiv.org/abs/2211.11866arxiv:2211.11866Mon, 21 Nov 2022 00:00:00 GMTLuke Thomas Peachey — Ricci flow spacetimes were introduced by Kleiner & Lott as a way to describe Ricci flow through singularities, and have since been used elsewhere in the literature, prompting the question of their rigidity. In (2+1)-dimensions, we show that every complete and sufficiently regular spacetime must be a cylindrical spacetime. That is, if the metric is complete on each spatial slice, after imposing a necessary continuity condition, we can conclude that every spatial slice must be diffeomorphic to a fixed surface, and the Ricci flow spacetime is isometric to a classical Ricci flow on this surface.Ricci flowSingularitiesWeak & singular flowsStability & uniqueness https://arxiv.org/abs/2205.03442arxiv:2205.03442Fri, 06 May 2022 00:00:00 GMTLuke Thomas Peachey — We formulate a uniqueness conjecture for curve shortening flow of proper curves on certain symmetric surfaces and give an example of a non-flat metric on the plane with respect to which curve shortening flow is not unique. That is, with respect to a suitably chosen metric, we construct a non-static solution to curve shortening flow starting from a properly embedded geodesic.Curve shorteningStability & uniqueness