Year: 2025
Type: preprint
Abstract: Inspired by Goette-Semmelmann \cite{GSSU2002}, we derive an estimate for the scalar curvature without a nonnegativity assumption on curvature operator. As an application, we show that, on an even dimensional closed manifold with nonzero Euler characteristic, any Riemannian metric $g$ is $ε$-gap distance extremal for some $ε\geq 0$. For manifolds with boundary, inspired by Lott \cite{JL2021}, we obtained a similar estimate for scalar curvature and mean curvature. We apply the estimate on certain Euclidean domains to study a Gromov's question in \cite{GM20233} concerning the extension problem of metric on the boundary to the interior.
Source: arXiv (Cornell University)
Authors: Sun, Yukai, Wang, Changliang
Institutions: Peking University, Tongji University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406033153