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<p>We prove that for a smooth convex body <i>K</i> ⊂ ℝ<sup><i>d</i></sup>, <i>d</i> ≥ 2, with positive Gauss curvature, its homothety with a certain associated convex body implies that <i>K</i> is either a ball or an ellipsoid, depending on the associated body considered.</p>

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Characterizations of balls and ellipsoids by infinitesimal homothetic conditions

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • M. Angeles Alfonseca,
  • Dmitry Ryabogin,
  • Alina Stancu,
  • Vladyslav Yaskin

摘要

We prove that for a smooth convex body K ⊂ ℝd, d ≥ 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.