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Parabolic classical curvature flows.

Guilfoyle, B. and Klingenberg, W. (2018) 'Parabolic classical curvature flows.', Journal of the Australian Mathematical Society., 104 (3). pp. 338-357.

Abstract

We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space, which evolve by an arbitrary (nonhomogeneous) function of the radii of curvature (RoC). We determine conditions for parabolic flows that ensure the boundedness of various geometric quantities and investigate some examples. As a new tool, we introduce the RoC diagram of a surface and its hyperbolic or anti-de Sitter metric. The relationship between the RoC diagram and the properties of Weingarten surfaces is also discussed.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1017/s1446788717000210
Publisher statement:This article has been published in a revised form in Journal of the Australian Mathematical Society https://doi.org/10.1017/s1446788717000210. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Australian Mathematical Publishing Association Inc 2017
Date accepted:29 January 2017
Date deposited:10 February 2017
Date of first online publication:30 October 2017
Date first made open access:30 April 2018

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