Differential and Integral Equations

Prescribing Gauss-Kronecker curvature on group invariant convex hypersurfaces

Richard Mikula

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 35J60: Nonlinear elliptic equations 58J05: Elliptic equations on manifolds, general theory [See also 35-XX]


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

Export citation