16th Panhellenic Geometry Conference

Some results on the $L_p$-Brunn-Minkowski inequality for intrinsic volumes and the $L_p$-Christosffel-Minkowski problem

Not scheduled

40m

Amphitheatre "Konstantin Karatheodory" (Department of Mathematics, NKUA)

Speaker

Konstantinos Patsalos (University of Ioannina)

Description

Our goal is to show how to improve some results related to the title of this talk, due to Bianchini, Colesanti, Pagnini and Roncoroni. Namely, we prove the log-Brunn-Minkowski inequality for intrinsic volumes (in fact the $L_p$-Brunn-Minkowski inequality for negative $p$) in a $C^2$ neighbourhood of the euclidean ball. On the other hand, we show that the $L_p$-Brunn-Minkowski inequality for intrinsic volumes does not hold globally for any $p<1$. Related, we prove a global uniqueness result for the $L_p$-Christoffel-Minkowski when the function in the right hand side is sufficiently close to the constant 1. Joint work with Christos Saroglou.