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Durham University

Department of Mathematical Sciences


Publication details for Wilhelm Klingenberg

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

Author(s) from Durham


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.