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$L^\infty$-metrics on tori and Schoen's conjecture
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-t
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