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- W3155118934 abstract "Abstract Consider a compact manifold $M$ with smooth boundary $partial M$. Suppose that $g$ and $tilde{g}$ are two Riemannian metrics on $M$. We construct a family of metrics on $M$ that agrees with $g$ outside a neighborhood of $partial M$ and agrees with $tilde{g}$ in a neighborhood of $partial M$. We prove that the family of metrics preserves various natural curvature conditions under suitable assumptions on the boundary data. Moreover, under suitable assumptions on the boundary data, we can deform a metric to one with totally geodesic boundary while preserving various natural curvature conditions." @default.
- W3155118934 created "2021-04-26" @default.
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- W3155118934 date "2021-04-13" @default.
- W3155118934 modified "2023-10-18" @default.
- W3155118934 title "Positivity of Curvature On Manifolds With Boundary" @default.
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- W3155118934 doi "https://doi.org/10.1093/imrn/rnab071" @default.
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