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1 September 2021 Evolution of noncompact hypersurfaces by inverse mean curvature
Beomjun Choi, Panagiota Daskalopoulos
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Duke Math. J. 170(12): 2755-2803 (1 September 2021). DOI: 10.1215/00127094-2020-0081

Abstract

We study the evolution of complete, noncompact, convex hypersurfaces in Rn+1 by the inverse mean curvature flow. We establish the long-time existence of solutions, and we provide the characterization of the maximal time of existence in terms of the tangent cone at infinity of the initial hypersurface. Our proof is based on an a priori pointwise estimate on the mean curvature of the solution from below in terms of the aperture of a supporting cone at infinity. The strict convexity of convex solutions is shown by means of viscosity solutions. Our methods also give an alternative proof of a result by Huisken and Ilmanen on compact star-shaped solutions.

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Beomjun Choi. Panagiota Daskalopoulos. "Evolution of noncompact hypersurfaces by inverse mean curvature." Duke Math. J. 170 (12) 2755 - 2803, 1 September 2021. https://doi.org/10.1215/00127094-2020-0081

Information

Received: 17 December 2018; Revised: 25 August 2020; Published: 1 September 2021
First available in Project Euclid: 7 July 2021

Digital Object Identifier: 10.1215/00127094-2020-0081

Subjects:
Primary: 53E10
Secondary: 35K55

Keywords: inverse mean curvature flow , noncompact

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 12 • 1 September 2021
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