A. Colesanti

activity

20052025

most citedThe

L_{p}

-Minkowski problem for

- n < p < 1

66 citations · 383 across the 32 of their papers we have counts for

collaborators

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18 papers · 1 filter

math.MG2024

The homogeneous decomposition of dually translation invariant valuations on Lipschitz functions on the sphere

Andrea Colesanti, Jonas Knoerr, Daniele Pagnini

We show that every continuous and dually translation invariant valuation on the space of Lipschitz functions on the unit sphere of $R^{n}$ , $n \geq 2$ , can be decomposed unique…

math.MG2021

On $p$ -Brunn-Minkowski inequalities for intrinsic volumes with $0 \leq p < 1$

C. Bianchini, A. Colesanti, D. Pagnini +1

We prove the validity of the $p$ -Brunn-Minkowski inequality for the intrinsic volume $V_{k}$ , $k = 2, \dots, n - 1$ , of convex bodies in $R^{n}$ , in a neighborhood of the unit ball…

math.MG2020

Continuous valuations on the space of Lipschitz functions on the sphere

Andrea Colesanti, Daniele Pagnini, Pedro Tradacete +1

We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere $S^{n - 1}$ . After introducing an appropriate notion of convergence, we show that c…

math.MG2019★ 40 cited

A homogeneous decomposition theorem for valuations on convex functions

A. Colesanti, M. Ludwig, F. Mussnig

The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation inva…

math.MG2017★ 21 cited

Hessian valuations

A. Colesanti, M. Ludwig, F. Mussnig

A new class of continuous valuations on the space of convex functions on $R^{n}$ is introduced. On smooth convex functions, they are defined for $i = 0, \dots, n$ by \begin{equa…

math.MG2017★ 22 cited

Smoothness in the $l_{p}$ Minkowski problem for $p < 1$

Gabriele Bianchi, Károly J. Böröczky, Andrea Colesanti

We discuss the smoothness and strict convexity of the solution of the $L_{p}$ Minkowski problem when $p < 1$ and the given measure has a positive density function.