We prove that for a smooth convex body $K \subset \mathbb{R}^d, d\geq 2,$ with positive Gauss curvature, its homothety with a certain associated convex body implies that $K$ is either a ball or an ellipsoid, depending on the associated body considered.
M. Angeles Alfonseca
,
Dmitry Ryabogin
,
Alina Stancu
,
Vladyslav Yaskin
. CHARACTERIZATIONS OF BALLS AND ELLIPSOIDS BY INFINITESIMAL HOMOTHETIC CONDITIONS[J]. Acta mathematica scientia, Series B, 2025
, 45(1)
: 280
-290
.
DOI: 10.1007/s10473-025-0122-x
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