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Parabolic Classical Curvature Flows

Guilfoyle, B.; Klingenberg, W.

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B. Guilfoyle


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.


Guilfoyle, B., & Klingenberg, W. (2018). Parabolic Classical Curvature Flows. Journal of the Australian Mathematical Society, 104(3), 338-357.

Journal Article Type Article
Acceptance Date Jan 29, 2017
Online Publication Date Oct 30, 2017
Publication Date Jun 1, 2018
Deposit Date Jan 26, 2017
Publicly Available Date Apr 30, 2018
Journal Journal of the Australian Mathematical Society
Print ISSN 1446-7887
Electronic ISSN 1446-8107
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 104
Issue 3
Pages 338-357
Related Public URLs


Accepted Journal Article (191 Kb)

Copyright Statement
This article has been published in a revised form in Journal of the Australian Mathematical Society 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

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