6 papers
Integral inequalities for -convolutions of -concave functions
Mokshay Madiman, Auttawich Manui, Bartłomiej Zawalski +1
Classical sumset inequalities originating in additive combinatorics admit geometric analogues for convex bodies in finite-dimensional real vector spaces, as recently developed by F…
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 flat shadow boundaries from point light sources and the characterization of ellipsoids
BartÅomiej 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…
Differential characterization of quadratic surfaces
BartÅomiej Zawalski
Let be a function defined on a connected open subset . We will show that its graph is contained in a quadratic surface if…
On the homothety conjecture for the body of flotation and the body of buoyancy on a plane
BartÅomiej Zawalski
We investigate several closely related "homothety conjectures" for convex bodies on a plane. Using the modern language of differential geometry, we systematically derive the fundam…
On star-convex bodies with rotationally invariant sections
BartÅomiej 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…