Work

Parabolic Classical Curvature Flows

Year: 2017

Type: article

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.

Source: Journal of the Australian Mathematical Society

DOI: 10.1017/s1446788717000210

Authors: BRENDAN GUILFOYLE, WILHELM KLINGENBERG

Institutions: Munster Technological University, Institute of Technology Tralee, Durham University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W1565358024

FWCI: 0.397

Cites: 24

Cited by: 6

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