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New monotonicity for $p$-capacitary functions in $3$-manifolds with nonnegative scalar curvature
- Publication Year :
- 2023
-
Abstract
- In this paper, we derive general monotone quantities and geometric inequalities associated with $p$-capacitary functions in asymptotically flat $3$-manifolds with simple topology and nonnegative scalar curvature. The inequalities become equalities on the spatial Schwarzschild manifolds outside rotationally symmetric spheres. This generalizes Miao's result \cite{M} from $p=2$ to $p\in (1, 3)$. As applications, we recover mass-to-$p$-capacity and $p$-capacity-to-area inequalities due to Bray-Miao \cite{BM} and Xiao \cite{Xiao}.<br />Comment: In this version, we extended the range of $k$ from $[0, 1]$ to $(-1, 1]$ in Theorem 1.1. As a consequence, we removed the assumption of nonnegative Hawking mass in Theorem 1.3
- Subjects :
- Mathematics - Differential Geometry
Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2306.00744
- Document Type :
- Working Paper