https://neckpinch.com/authors/carlo-sinestrari/New arXiv papers by Carlo Sinestrari, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.20265arxiv:2610.20265Wed, 14 Oct 2026 00:00:00 GMTEsther Cabezas-Rivas, Carlo Sinestrari — We prove stability of geodesic spheres under volume-preserving mean curvature flow in the simply connected space forms under genuinely first-order geometric assumptions. The initial hypersurface is required to lie in a sufficiently thin annulus around a geodesic sphere and to have outward normal making a small angle with the radial direction. No convexity, mean convexity, initial curvature bound, or Hölder control of the normal is assumed. The main ingredient is a quantitative Alexandrov reflection argument that converts these initial assumptions into a strong reflection property preserved by the flow. The resulting radial and angular control allows us to derive estimates for the mean curvature and the full second fundamental form, and hence long-time existence, eventual convexity, and smooth exponential convergence to a geodesic sphere. In hyperbolic space, the eventual convexity can be strengthened to horospherical convexity. The reflection threshold also yields a quantitative estimate for the displacement of the limiting centre. For Lipschitz initial hypersurfaces, we develop a separate positive-time curvature estimate that is uniform along smooth approximations. This produces an instantaneously smooth evolution with the same eventual convexity and smooth exponential convergence.Mean curvature flowVolume-preserving & constrained flowsSphere theoremsStability & uniquenessLong-time existence & convergence https://arxiv.org/abs/2501.13091arxiv:2501.13091Wed, 22 Jan 2025 00:00:00 GMTCarlo Sinestrari, Jacopo Tenan — We study the volume preserving mean curvature flow of a surface immersed in an asymptotically flat 3-manifold modeling an isolated gravitating system in General Relativity. We show that, if the ambient manifold has positive ADM mass and the initial surface is round in a suitable sense, then the flow exists for all times and converges smoothly to a stable CMC surface. This extends to the asymptotically flat setting a classical result by Huisken-Yau (Invent. Math. 1996) and allows to construct a CMC foliation of the outer part of the manifold by an alternative approach to the ones by Nerz (Calc. Var. PDE, 2015) or by Eichmair-Koerber (J. Diff. Geometry, 2024).Mean curvature flowVolume-preserving & constrained flowsBoundaries & non-compactLong-time existence & convergenceMinimal & CMC surfacesPhysics https://arxiv.org/abs/2405.02722arxiv:2405.02722Sat, 04 May 2024 00:00:00 GMTCarlo Sinestrari, Liangjun Weng — In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mean curvature with a non-local averaging term. We demonstrate that for any convex initial hypersurface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as t → +∞Mean curvature flowOther curvature flowsVolume-preserving & constrained flowsFree boundary & capillaryLong-time existence & convergence https://arxiv.org/abs/2203.05259arxiv:2203.05259Thu, 10 Mar 2022 00:00:00 GMTSusanna Risa, Carlo Sinestrari — We prove the existence of closed convex ancient solutions to curvature flows which become more and more oval for large negative times. The speed function is a general symmetric function of the principal curvatures, homogeneous of degree greater than one. This generalises previous work on the mean curvature flow and other one-homogeneous curvature flows. As an auxiliary result, we prove a new theorem on the convergence to a round point of convex rotationally symmetric hypersurfaces satisfying a suitable constraint on the curvatures.Mean curvature flowOther curvature flowsAncient solutionsHomogeneous spacesRotational symmetry & warped products