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Locally constrained inverse curvature flows

Scheuer, Julian and Xia, Chao 2019. Locally constrained inverse curvature flows. Transactions of the American Mathematical Society 372 (10) , pp. 6771-6803. 10.1090/tran/7949
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We consider inverse curvature flows in warped product manifolds, which are constrained subject to local terms of lower order--namely, the radial coordinate and the generalized support function. Under various assumptions we prove longtime existence and smooth convergence to a coordinate slice. We apply this result to deduce a new Minkowski-type inequality in the anti-de Sitter Schwarzschild manifolds and a weighted isoperimetric-type inequality in hyperbolic space.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Mathematics
Publisher: American Mathematical Society
ISSN: 0002-9947
Funders: Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)
Date of First Compliant Deposit: 8 October 2020
Date of Acceptance: 10 July 2019
Last Modified: 13 Oct 2020 09:45

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