PreprintarXiv licencearXiv
L∞-metrics on tori and Schoen's conjecture
Abstract
We prove Schoen's conjecture on L∞-metrics for tori. More precisely, we show that any L∞-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∞-metric. Our proof uses weighted scalar curvature and the relative index theorem.
Related
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BibTeX
@misc{wang2026lmetrics,
title = {{$L^\infty$-metrics on tori and Schoen's conjecture}},
author = {Jian Wang and Jinmin Wang and Zhizhang Xie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.21325},
eprint = {2606.21325},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21325},
}
RIS
TY - UNPB
TI - L^∞-metrics on tori and Schoen's conjecture
AU - Jian Wang
AU - Jinmin Wang
AU - Zhizhang Xie
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2606.21325
UR - https://arxiv.org/abs/2606.21325
AB - We prove Schoen's conjecture on L^∞-metrics for tori. More precisely, we show that any L^∞-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^∞-metric. Our proof uses weighted scalar curvature and the relative index theorem.
ER -