International Mathematics Research Notices ( IF 1.452 ) Pub Date : 2017-11-15 , DOI: 10.1093/imrn/rnx284
Li Q.

We study the multiplicity result for the centro-affine Minkowski problem. It is well-known that all ellipsoids with constant volume have the same centro-affine curvature. In this article, we construct a positive, Hölder continuous function $f\in C^\alpha (\mathbb S^n)$ such that there are infinitely many $C^{2,\alpha}$ hypersurfaces which are not affine-equivalent, but have the same centro-affine curvature $1/f$.

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