Parabolic Classical Curvature Flows

Guilfoyle, B.; Klingenberg, W.

doi:10.1017/s1446788717000210

Parabolic Classical Curvature Flows

Guilfoyle, B.; Klingenberg, W.

Authors

B. Guilfoyle

Dr Wilhelm Klingenberg wilhelm.klingenberg@durham.ac.uk
Associate Professor

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.

Citation

Guilfoyle, B., & Klingenberg, W. (2018). Parabolic Classical Curvature Flows. Journal of the Australian Mathematical Society, 104(3), 338-357. https://doi.org/10.1017/s1446788717000210

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
DOI	https://doi.org/10.1017/s1446788717000210
Related Public URLs	https://arxiv.org/abs/1503.01930

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Copyright 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