Advances in Differential Equations

Complete noncompact self-similar solutions of Gauss curvature flows II. Negative powers

John Urbas

Full-text: Open access

Abstract

We classify all complete noncompact embedded convex hypersurfaces in $\mathbf{R}^{n+1}$ which move homothetically under flow by some negative power of their Gauss curvature.

Article information

Source
Adv. Differential Equations, Volume 4, Number 3 (1999), 323-346.

Dates
First available in Project Euclid: 15 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366031038

Mathematical Reviews number (MathSciNet)
MR1671253

Zentralblatt MATH identifier
0957.53033

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 35J60: Nonlinear elliptic equations 35K55: Nonlinear parabolic equations 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C45: Global surface theory (convex surfaces à la A. D. Aleksandrov)

Citation

Urbas, John. Complete noncompact self-similar solutions of Gauss curvature flows II. Negative powers. Adv. Differential Equations 4 (1999), no. 3, 323--346. https://projecteuclid.org/euclid.ade/1366031038


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