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pro vyhledávání: '"Caputo, Emanuele"'
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in both cases a
Externí odkaz:
http://arxiv.org/abs/2409.03698
Autor:
Caputo, Emanuele, Cavallucci, Nicola
We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, $\varepsilon$-chains are a finite collection of points with distance at most $\varepsilon$ between consecutive point
Externí odkaz:
http://arxiv.org/abs/2408.15071
Autor:
Caputo, Emanuele, Cavallucci, Nicola
The goal of this paper is to continue the study of the relation between the Poincar\'e inequality and the lower bounds of Minkowski content of separating sets, initiated in our previous work [Caputo, Cavallucci: Poincar\'e inequality and energy of se
Externí odkaz:
http://arxiv.org/abs/2402.18327
Autor:
Caputo, Emanuele, Cavallucci, Nicola
We study geometric characterizations of the Poincar\'{e} inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set separating them, such properties are formulated in terms of several po
Externí odkaz:
http://arxiv.org/abs/2401.02762
A finite-dimensional ${\sf RCD}$ space can be foliated into sufficiently regular leaves, where a differential calculus can be performed. Two important examples are given by the measure-theoretic boundary of the superlevel set of a function of bounded
Externí odkaz:
http://arxiv.org/abs/2308.12042
We study extensions of sets and functions in general metric measure spaces. We show that an open set has the strong BV extension property if and only if it has the strong extension property for sets of finite perimeter. We also prove several implicat
Externí odkaz:
http://arxiv.org/abs/2302.10018
Autor:
Caputo, Emanuele, Rossi, Tommaso
In this paper, we prove first-order asymptotics on a bounded open set of the heat content when the ambient space is an ${\sf RCD}(K,N)$ space, under a regularity condition for the boundary that we call measured interior geodesic condition of size $\e
Externí odkaz:
http://arxiv.org/abs/2212.06059
We provide a general theory for parallel transport on non-collapsed ${\sf RCD}$ spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and, more generally, of curves obtained via the flow of sufficiently regul
Externí odkaz:
http://arxiv.org/abs/2108.07531
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