Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Ulivelli, Jacopo"'
Autor:
Knoerr, Jonas, Ulivelli, Jacopo
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the support of
Externí odkaz:
http://arxiv.org/abs/2408.06946
We prove a functional version of the additive kinematic formula as an application of the Hadwiger theorem on convex functions together with a Kubota-type formula for mixed Monge-Amp\`ere measures. As an application, we give a new explanation for the
Externí odkaz:
http://arxiv.org/abs/2403.06697
The Rogers-Shephard and Zhang's projection inequalities are two reverse, affine isoperimetric inequalities relating the volumes of a convex body and its difference body and polar projection body, respectively. Following a classical work by Schneider,
Externí odkaz:
http://arxiv.org/abs/2403.05712
Motivated by a problem for mixed Monge-Amp\`ere measures of convex functions, we address a special case of a conjecture of Schneider and show that for every convex body $K$ the support of the mixed area measure $S(K[j],B_L^{n-1}[n-1-j],\cdot)$ is giv
Externí odkaz:
http://arxiv.org/abs/2401.16371
Autor:
Ulivelli, Jacopo
We introduce functional Wulff shapes based on the classical construction for compact convex sets. With this new tool, we establish a functional version of Aleksandrov's variational lemma in the family of convex functions with compact domain. The resu
Externí odkaz:
http://arxiv.org/abs/2312.11172
Autor:
Ulivelli, Jacopo
In this short note, we prove the existence of solutions to a Monge-Amp\`ere equation of entire type derived by a weighted version of the classical Minkowski problem.
Externí odkaz:
http://arxiv.org/abs/2310.02787
Autor:
Langharst, Dylan, Ulivelli, Jacopo
The interplay between variational functionals and the Brunn-Minkowski Theory is a well-established phenomenon widely investigated in the last thirty years. In this work, we prove the existence of solutions to the even logarithmic Minkowski problems a
Externí odkaz:
http://arxiv.org/abs/2304.02548
Autor:
Knoerr, Jonas, Ulivelli, Jacopo
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by McMullen can be used to obtain a characterization of continuous, epi-translation invariant, and n-epi-h
Externí odkaz:
http://arxiv.org/abs/2301.10049
Autor:
Ulivelli, Jacopo
Steiner symmetrization is well known for its rounding and general convergence properties. We identify a whole family of symmetrizations sharing analogue behaviors: In fact we prove that all these symmetrizations share the same converging symmetrizati
Externí odkaz:
http://arxiv.org/abs/2207.05416
Autor:
Ulivelli, Jacopo
We shall prove a convergence result relative to sequences of Minkowski symmetrals of general compact sets. In particular, we investigate the case when this process is induced by sequences of subspaces whose elements belong to a finite family, followi
Externí odkaz:
http://arxiv.org/abs/2007.04307