Differential and Integral Equations

Prescribing Gauss-Kronecker curvature on group invariant convex hypersurfaces

Richard Mikula

Abstract

We consider the problem of prescribing Gauss-Kronecker curvature in Euclidean space. In particular, by a degree theory argument, we prove the existence of a closed convex hypersurface in $\mathbb{R}^{3}$ which has its Gauss-Kronecker curvature equal to $F$, a prescribed positive function, which is invariant under a fixed-point free subgroup $G$ of the orthogonal group $O(3)$, requiring that $F$ satisfy natural growth assumptions near the origin and at infinity.

Article information

Source
Differential Integral Equations, Volume 19, Number 10 (2006), 1103-1128.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050311

Mathematical Reviews number (MathSciNet)
MR2278672

Zentralblatt MATH identifier
1212.53083

Citation

Mikula, Richard. Prescribing Gauss-Kronecker curvature on group invariant convex hypersurfaces. Differential Integral Equations 19 (2006), no. 10, 1103--1128. https://projecteuclid.org/euclid.die/1356050311