Proves Bezdek's conjecture in dimensions n≥3 for convex bodies with aligned center of symmetry, assuming sections through a fixed point have reflection axes whose complementary invariant subspaces are parallel to a fixed hyperplane, in both orthogonal and affine settings.
Zawalski, On star-convex bodies with rotationally invariant sections , Beitr¨ age zur Algebra und Geometrie65 (2024), 495–509
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On Bezdek's conjecture for high-dimensional convex bodies with an aligned center of symmetry
Proves Bezdek's conjecture in dimensions n≥3 for convex bodies with aligned center of symmetry, assuming sections through a fixed point have reflection axes whose complementary invariant subspaces are parallel to a fixed hyperplane, in both orthogonal and affine settings.