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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Locally constrained inverse curvature flows
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by Julian Scheuer and Chao Xia PDF
Trans. Amer. Math. Soc. 372 (2019), 6771-6803 Request permission

Abstract:

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.
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Additional Information
  • Julian Scheuer
  • Affiliation: Albert-Ludwigs-Universität, Mathematisches Institut, Abteilung Reine Mathematik, Ernst-Zermelo-Stra\normalfont{ß}e 1, 79104 Freiburg, Germany
  • MR Author ID: 1104274
  • Email: julian.scheuer@math.uni-freiburg.de
  • Chao Xia
  • Affiliation: School of Mathematical Sciences, Xiamen University, 361005 Xiamen, People’s Republic of China
  • MR Author ID: 922365
  • Email: chaoxia@xmu.edu.cn
  • Received by editor(s): August 20, 2017
  • Published electronically: August 28, 2019
  • Additional Notes: The first author was being supported by the “Deutsche Forschungsgemeinschaft” (DFG, German research foundation), research grant “Quermassintegral preserving local curvature flows”, number SCHE 1879/3-1. The research of the second author was supported in part by NSFC (Grant No. 11501480, 11871406), the Natural Science Foundation of Fujian Province of China (Grant No. 2017J06003) and the Fundamental Research Funds for the Central Universities (Grant No. 20720180009). Part of this work was done while he was visiting the Institute of Mathematics at Albert-Ludwigs-Universität Freiburg. He would like to thank the Institute for its hospitality.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 6771-6803
  • MSC (2010): Primary 53C21, 53C24, 53C44
  • DOI: https://doi.org/10.1090/tran/7949
  • MathSciNet review: 4024538