4 papers
John Ellipsoids of Revolution
Grigory Ivanov, Zsolt Lángi, Márton Naszódi +1
Finding a largest Euclidean ball in a given convex body and finding a largest volume ellipsoid in are two problems of fundamentally different nature. T…
The John inclusion for log-concave functions
G. Ivanov
John's inclusion states that a convex body in can be covered by the -dilation of its maximal volume ellipsoid. We obtain a certain John-type inclusion for log-con…
Helly numbers for Quantitative Helly-type results
G. Ivanov, M. Naszodi
We obtain three Helly-type results. First, we establish a Quantitative Colorful Helly-type theorem with the optimal Helly number \(2d\) concerning the diameter of the intersection…
No-dimensional Helly's theorem in uniformly convex Banach spaces
G. Ivanov
We study the ``no-dimensional'' analogue of Helly's theorem in Banach spaces. Specifically, we obtain the following no-dimensional Helly-type results for uniformly convex Banach sp…