Year: 2026
Type: preprint
Abstract: We prove Schoen's conjecture on $L^\infty$-metrics for tori. More precisely, we show that any $L^\infty$-metric on a torus that is smooth and has non-negative scalar curvature away from an embedded submanifold with codimension at least three extends to a smooth flat metric. We also prove a LLarull-type theorem for $L^\infty$-metric. Our proof uses weighted scalar curvature and the relative index theorem.
Source: arXiv (Cornell University)
Authors: Wang, Jian, Wang, Jinmin, Xie, Zhizhang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165634500