https://neckpinch.com/authors/jacopo-tenan/New arXiv papers by Jacopo Tenan, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2607.02244arxiv:2607.02244Thu, 02 Jul 2026 00:00:00 GMTJacopo Tenan — We construct an exhaustive family of constant spacetime mean curvature (STCMC) surfaces for initial data sets close to the anti-de Sitter-Schwarzschild hyperboloid. In particular, we obtain such a foliation as the long time limit of the volume preserving spacetime mean curvature flow starting from the constant mean curvature foliation constructed by Neves-Tian (Geom. Funct. Anal., 2009). As an application, inspired by the definition of STCMC center of mass for initial data sets proposed in the asymptotically Euclidean setting by Cederbaum-Sakovich (Calc. Var. PDE, 2021), we study the center of mass of an asymptotically hyperboloidal initial data set.Mean curvature flowPhysics 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/2407.12971arxiv:2407.12971Wed, 17 Jul 2024 00:00:00 GMTJacopo Tenan — We consider a volume preserving curvature evolution of surfaces in an asymptotically Euclidean initial data set with positive ADM-energy. The speed is given by a nonlinear function of the mean curvature which generalizes the spacetime mean curvature recently considered by Cederbaum-Sakovich (Calc. Var. PDE, 2021). Following a classical approach by Huisken-Yau (Invent. Math., 1996), we show that the flow starting from suitably round initial surfaces exists for all times and converges to a constant (spacetime) curvature limit. This provides an alternative construction of the CSTMC foliation by Cederbaum-Sakovich and has applications in the definition of center of mass of an isolated system in General Relativity.Mean curvature flowVolume-preserving & constrained flowsLong-time existence & convergencePhysics