1 citations · 2 across the 8 of their papers we have counts for
9 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 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 the homothety conjecture for the body of flotation and the body of buoyancy on a plane
Bartłomiej 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 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…
Differential characterization of quadratic surfaces
Bartłomiej Zawalski
Let be a function defined on a connected open subset . We will show that its graph is contained in a quadratic surface if an…
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…
The $H^1(\T^d)$-multiplier norm of Rajchman measures, Zafran-type phenomena, and Walsh--Stieltjes series
Przemysław Ohrysko, Michał Wojciechowski, Bartłomiej Zawalski
We study convolution by complex Rajchman measures as Fourier multipliers on the mean-zero part of the classical isotropic Hardy space $H^1(\T^d)$. Our main technical result gives a…
A concise formula for the Hessian determinant of a function parameterising a quadratic hypersurface
Bartłomiej Zawalski
We will give a concise formula for the Hessian determinant of a smooth function such that its graph is contained in a quadratic hypersurface.…