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On flat shadow boundaries from point light sources and the characterization of ellipsoids
Bartłomiej Zawalski
In his classical work, W. Blaschke proved that a convex body whose shadow boundaries are flat for every direction of parallel illumination must be an ellipsoid. An extension recent…
On Bezdek's conjecture for high-dimensional convex bodies with an aligned center of symmetry
M. Angeles Alfonseca, B. Zawalski
In 1999, K. Bezdek posed a conjecture stating that among all convex bodies in , ellipsoids and bodies of revolution are characterized by the fact that all their planar…
On separably integrable symmetric convex bodies
Vladyslav Yaskin, Bartłomiej Zawalski
An infinitely smooth symmetric convex body is called -separably integrable, , if its -dimensional isotropic volume function $V_{K,H}(t)=\math…
On star-convex bodies with rotationally invariant sections
Bartłomiej Zawalski
We will prove that an origin-symmetric star-convex body with sufficiently smooth boundary and such that every hyperplane section of passing through the origin is a body of…