66 citations · 383 across the 32 of their papers we have counts for
8 papers · 1 filter
Hessian valuations
A. Colesanti, M. Ludwig, F. Mussnig
A new class of continuous valuations on the space of convex functions on is introduced. On smooth convex functions, they are defined for by \begin{equa…
A note on the quantitative local version of the log-Brunn-Minkowski inequality
Andrea Colesanti, Galyna V. Livshyts
We prove that the log-Brunn-Minkowski inequality \begin{equation*} |λK+_0 (1-λ)L|\geq |K|^λ|L|^{1-λ} \end{equation*} (where is the Lebesgue measure and is the so-ca…
The -Minkowski problem for
Gabriele Bianchi, Károly J. Böröczky, Andrea Colesanti +1
Chou and Wang's existence result for the -Minkowski problem on for and an absolutely continuous measure is discussed and extended to more…
Minkowski valuations on convex functions
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A classification of SL contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measur…
Smoothness in the Minkowski problem for
Gabriele Bianchi, Károly J. Böröczky, Andrea Colesanti
We discuss the smoothness and strict convexity of the solution of the Minkowski problem when and the given measure has a positive density function.
Translation invariant valuations on quasi-concave functions
Andrea Colesanti, Nico Lombardi, Lukas Parapatits
We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of N variables. In particular, we prove a homogeneous decompos…