16 citations · 45 across the 24 of their papers we have counts for
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The Logarithmic Minkowski conjecture and the -Minkowski Problem
Karoly J. Boroczky
The current state of art concerning the Minkowski problem as a Monge-Ampere equation on the sphere and Lutwak's Logarithmic Minkowski conjecture about the uniqueness of even…
Convex bodies of constant width in spaces of constant curvature and the extremal area of Reuleaux triangles
Karoly J. Boroczky, Adam Sagmeister
Extending Blaschke and Lebesgue's classical result in the Euclidean plane, it has been recently proved in spherical and the hyperbolic cases, as well, that Reuleaux triangles have…
The case of equality in geometric instances of Barthe's reverse Brascamp-Lieb inequalit
Karoly J. Boroczky, Pavlos Kalantzopoulos, Dongmeng Xi
The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the…
A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions
Károly J. Böröczky, Alessio Figalli, João P. G. Ramos
We prove that if a triplet of functions satisfies almost equality in the Prékopa-Leindler inequality, then these functions are close to a common log-concave function, up to multipl…