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Scalar curvature rigidity of small spherical caps with arbitrary fill-ins
We prove an analogue of Min-Oo's conjecture for sufficiently small spherical caps in the unit round sphere. For every dimension $n\ge3$, there exists $r_*(n)>0$ such that the following holds for every round cap of radius $0<r\le r_*(n)$: any smooth compact connected oriented Riemannian fill-in with
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