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.
Rogers, Sections and projections of convex bodies , Portugaliae Mathematica 24 (1965), no
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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.