Guilfoyle, B. and Klingenberg, W. (2018) 'Parabolic classical curvature flows.', Journal of the Australian Mathematical Society., 104 (3). pp. 338-357.
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.
|Full text:||(AM) Accepted Manuscript|
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|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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