Paper · Jul 2, 2026
Foliations by constant spacetime mean curvature surfaces for asymptotically hyperboloidal initial data sets
As on arXiv
Abstract
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.
Comments: Comments are welcome! Decay hypothesis improved with respect to the author's talk at the KTH conference "Geometric Analysis: Parabolic and Elliptic Methods", June 2026
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Volume preserving spacetime mean curvature flow and foliations of initial data sets
Topics Physics · Same author Jacopo Tenan · Shared terms “spacetime mean”, “data set”, “preserving spacetime”
-
Foliations of asymptotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature
Topics Mean curvature flow · Shared terms “constant spacetime”, “spacetime mean”, “STCMC”
-
Foliation of constant harmonic mean curvature surfaces in asymptotic Schwarzschild spaces
Topics Physics · Shared terms “curvature surface”, “data set”, “foliation”
-
Hawking Mass Monotonicity for Initial Data Sets
Topics Physics · Shared terms “data set”, “initial data”, “foliation”
-
Volume preserving mean curvature flow of round surfaces in asymptotically flat spaces
Topics Physics · Same author Jacopo Tenan · Shared terms “volume preserving”, “foliation”, “Calc”
-
On the evolution of hypersurfaces along their inverse spacetime mean curvature
Topics Physics · Shared terms “spacetime mean”, “data set”, “initial data”
-
A CMC existence result for expanding cosmological spacetimes
Topics Physics · Shared terms “constant mean”
-
Mean Curvature Flow in de Sitter space
Topics Physics · Shared terms “Sitter”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.