Startseite Mathematik Minkowski inequalities and constrained inverse curvature flows in warped spaces
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Minkowski inequalities and constrained inverse curvature flows in warped spaces

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Veröffentlicht/Copyright: 28. Oktober 2020

Abstract

This paper deals with locally constrained inverse curvature flows in a broad class of Riemannian warped spaces. For a certain class of such flows, we prove long-time existence and smooth convergence to a radial coordinate slice. In the case of two-dimensional surfaces and a suitable speed, these flows enjoy two monotone quantities. In such cases, new Minkowski type inequalities are the consequence. In higher dimensions, we use the inverse mean curvature flow to obtain new Minkowski inequalities when the ambient radial Ricci curvature is constantly negative.

MSC 2010: 39B62; 53C21; 53C44

Award Identifier / Grant number: SCHE 1879/3-1

Funding statement: Funded by the “Deutsche Forschungsgemeinschaft” (DFG, German research foundation), project “Quermassintegral preserving local curvature flows”, grant number SCHE 1879/3-1.

Acknowledgements

This work was made possible through a research scholarship the author received from the DFG and which was carried out at Columbia University in New York. J. Scheuer would like to thank the DFG, Columbia University and especially Prof. Simon Brendle for their support.

  1. Communicated by: Guofang Wang

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Received: 2020-05-22
Accepted: 2020-10-06
Published Online: 2020-10-28
Published in Print: 2022-10-01

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