Constant Harmonic Mean Curvature Foliation in Asymptotic Schwarzschild Spaces-II
Differential Geometry
2025-05-29 v2
Abstract
This paper extends the results of [GLS24], where the existence of a constant harmonic mean curvature foliation was established in the setting of a 3-dimensional asymptotically Schwarzschild manifold. Here, we generalize this construction to higher dimensions, proving the existence of foliations by constant harmonic mean curvature hypersurfaces in an asymptotically Schwarzschild manifold of arbitrary dimension. Furthermore, in 3 dimensional case, we demonstrate the local uniqueness of this foliation under a stronger decay conditions on the asymptotically Schwarzschild metric
Keywords
Cite
@article{arxiv.2505.19181,
title = {Constant Harmonic Mean Curvature Foliation in Asymptotic Schwarzschild Spaces-II},
author = {Yaoting Gui and Yuqiao Li and Jun Sun},
journal= {arXiv preprint arXiv:2505.19181},
year = {2025}
}
Comments
Comments are welcome. arXiv admin note: text overlap with arXiv:2412.17024