18 citations · 26 across the 7 of their papers we have counts for
8 papers
Busemann's intersection inequality in hyperbolic and spherical spaces
Susanna Dann, Jaegil Kim, Vladyslav Yaskin
Busemann's intersection inequality asserts that the only maximizers of the integral among all convex bodies of a fixed volume in …
Distribution functions of sections and projections of convex bodies
Jaegil Kim, Vladyslav Yaskin, Artem Zvavitch
Typically, when we are given the section (or projection) function of a convex body, it means that in each direction we know the size of the central section (or projection) perpendi…
On the local convexity of intersection bodies of revolution
M. Angeles Alfonseca, Jaegil Kim
One of the fundamental results in Convex Geometry is Busemann's theorem, which states that the intersection body of a symmetric convex body is convex. Thus, it is only natural to a…
Stability of the reverse Blaschke-Santalo inequality for unconditional convex bodies
Jaegil Kim, Artem Zvavitch
Mahler's conjecture asks whether the cube is a minimizer for the volume product of a body and its polar in the class of symmetric convex bodies in R^n. The corresponding inequality…
Minimal volume product near Hanner polytopes
Jaegil Kim
Mahler's conjecture asks whether the cube is a minimizer for the volume product of a body and its polar in the class of symmetric convex bodies in a fixed dimension. It is known th…
The geometry of p-convex intersection bodies
Jaegil Kim, Vladyslav Yaskin, Artem Zvavitch
Busemann's theorem states that the intersection body of an origin-symmetric convex body is also convex. In this paper we provide a version of Busemann's theorem for p-convex bodies…