'Ad'am Sagmeister

collaborators

4 papers

math.MG2026

PÃ¡l's isominwidth inequality for ball convex bodies in planes of constant curvature

Ferenc Fodor, Nathan Robock, ÃdÃ¡m Sagmeister

PÃ¡l's classical isominwidth inequality states that the regular triangle has minimal area among plane convex bodies of minimal width $w$ . A similar result is the Blaschke--Lebesgue…

math.MG2026

Optimal stability of PÃ¡l's isominwidth inequality for ball convex bodies in planes of constant curvature

Ferenc Fodor, ÃdÃ¡m Sagmeister

PÃ¡l's isominwidth inequality (1921) answered the Kakeya needle problem (1917) for convex sets. It states that among convex bodies of fixed minimum width $w$ in the Euclidean plane…

math.CO2025

Penny graphs in the hyperbolic plane

ÃdÃ¡m Sagmeister, Konrad J. Swanepoel

We consider the problem of finding the maximum number $e_{d} (n)$ of pairs of touching circles in a packing of $n$ congruent circles of diameter $d$ in the hyperbolic plane of curvatu…

math.MG2025

John Ellipsoids of Revolution

Grigory Ivanov, Zsolt LÃ¡ngi, MÃ¡rton NaszÃ³di +1

Finding a largest Euclidean ball in a given convex body $K \subset R^{d}$ and finding a largest volume ellipsoid in $K$ are two problems of fundamentally different nature. T…