Paper · Jul 8, 2019

A curvature flow approach to Lp-Christoffel-Minkowski problem for p>1

Li Chen, Qiang Tu, Ni Xiang

math.APWider flowsarXiv:1907.03649v3
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Abstract

We study the motion of smooth, closed, strictly convex hypersurfaces in Rn+1 expanding in the direction of their normal vector field with speed depending on the k-th elementary symmetric polynomial of the principal radii of curvature. As an application, we gives a unifed fow approach to Lp-Christoffel-Minkowski problem for p > 1.

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Submitted
Jul 8, 2019
Last revised
Jan 21, 2020 (v3)
Subjects
math.AP

Comments: There was an error in Section 3

Other curvature flowsGauss curvature flow

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Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974) Gauss curvature flow Wider flows Convex hypersurfaces shrink with normal speed a power K^α of their Gauss curvature. Firey proposed it as a model of stones worn by waves; for α>… Start with: Shapes of worn stones (Firey, 1974)