11 papers
The Lp centro-sectional Minkowski problem
Karoly J. Boroczky, Jiaqian Liu, Renqing You
As part of Lutwak's broadening of the Brunn-Minkowski theory, and extending the notion of affine quermassintegrals and dual curvature measure discussed by Milman, Yehudayoff and Hu…
On Ball's conjectured Santaló type inequality
Károly J. Böröczky, Konstantinos Patsalos, Christos Saroglou
We prove that if is a symmetric and isotropic convex body in , then $$\int_K\langle x,u\rangle^2\,dx\int_{K^\circ}\langle x,u\rangle^2\,dx\leq \left(\int_{B_2^n}\…
Quantitative Stability for Minkowski's problem
Károly Böröczky, João Miguel Machado, João P. G. Ramos
We derive quantitative stability results for Minkowski bodies, as well as their counterparts, the -Minkowski bodies in the range . We prove that, for every pai…
Quantitative stability of extremal quasi conformal mappings
Zoltán M. Balogh, Károly J. Böröczky, Ãgnes Mester
We establish quantitative stability results for classical distortion minimization problems in the theory of quasiconformal mappings. We consider the mean distortion functional and…
A strengthening of the Blaschke-Santaló inequality for -symmetric planar convex bodies
Károly J. Böröczky, Endre Makai
We verify the inequality for any -symmetric convex body where is either the John ellipse of maximal ar…
Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
Karoly J. Böröczky, Ferenc Fodor, Pavlos Kalantzopoulos
We use the characterization of the case of equality in Barthe's Geometric Reverse Brascamp-Lieb inequality to characterize equality in Liakopoulos's volume estimate in terms of sec…