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- W2523151313 abstract "We obtain some estimates on the area of the boundary and on the volume of a certain free boundary hypersurface $Sigma$ with nonpositive Yamabe invariant in a Riemannian $n$-manifold with bounds for the scalar curvature and the mean curvature of the boundary. Assuming further that $Sigma$ is locally volume-minimizing in a manifold $M^n$ with scalar curvature bounded below by a nonpositive constant and mean convex boundary, we conclude that locally $M$ splits along $Sigma$. In the case that the scalar curvature of $M$ is at least $-n(n-1)$ and $Sigma$ locally minimizes a certain functional inspired by [30], a neighborhood of $Sigma$ in $M$ is isometric to $((-varepsilon,varepsilon)timesSigma,dt^2+e^{2t}g)$, where $g$ is Ricci flat." @default.
- W2523151313 created "2016-09-30" @default.
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- W2523151313 date "2014-06-17" @default.
- W2523151313 modified "2023-09-26" @default.
- W2523151313 title "Free boundary hypersurfaces with nonpositive Yamabe invariant in mean convex manifolds" @default.
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