Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Brena, Camillo"'
Autor:
Brena, Camillo, Decio, Stefano
The main goal of this work is to prove an instance of the unique continuation principle for area minimizing integral currents. More precisely, consider an $m$-dimensional area minimizing integral current and an $m$-dimensional minimal surface, both c
Externí odkaz:
http://arxiv.org/abs/2406.07600
Autor:
Brena, Camillo, Gigli, Nicola
It is known that on $\mathrm{RCD}$ spaces one can define a distributional Ricci tensor ${\bf Ric}$. Here we give a fine description of this object by showing that it admits the polar decomposition $${\bf Ric}=\omega\,|{\bf Ric}|$$ for a suitable non-
Externí odkaz:
http://arxiv.org/abs/2310.07536
Autor:
Brena, Camillo, Gigli, Nicola
We give an alternative proof of the general chain rule for functions of bounded variation ([ADM90]), which allows to compute the distributional differential of $\varphi\circ F$, where $\varphi\in \mathrm{LIP}(\mathbb{R}^m)$ and $F\in\mathrm{BV}(\math
Externí odkaz:
http://arxiv.org/abs/2307.06008
We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincar\'e property, we produce a well-behaved relaxation theory via approximation by simple maps
Externí odkaz:
http://arxiv.org/abs/2306.00768
Autor:
Brena, Camillo, Pinamonti, Andrea
We extend Nguyen's characterization of Sobolev spaces $W^{1,p}$ to the setting of PI-metric measure spaces such that at a.e. point the tangent space (in the Gromov-Hausdorff sense) is unique and Euclidean with a fixed dimension. We also generalize [C
Externí odkaz:
http://arxiv.org/abs/2304.06561
In this paper we analyze in detail a few questions related to the theory of functions with bounded $p$-Hessian-Schatten total variation, which are relevant in connection with the theory of inverse problems and machine learning. We prove an optimal de
Externí odkaz:
http://arxiv.org/abs/2302.12554
In the setting of finite-dimensional $\mathrm{RCD}(K,N)$ spaces, we characterize the $p$-Sobolev spaces for $p\in(1,\infty)$ and the space of functions of bounded variation in terms of the short-time behaviour of the heat flow. Moreover, we prove tha
Externí odkaz:
http://arxiv.org/abs/2212.03910
In this paper, we characterize the class of extremal points of the unit ball of the Hessian-Schatten total variation (HTV) functional. The underlying motivation for our work stems from a general representer theorem that characterizes the solution set
Externí odkaz:
http://arxiv.org/abs/2210.04077
In this work we extend classical results for subgraphs of functions of bounded variation in $\mathbb{R}^n\times\mathbb{R}$ to the setting of $\mathsf{X}\times\mathbb{R}$, where $\mathsf{X}$ is an ${\rm RCD}(K,N)$ metric measure space. In particular,
Externí odkaz:
http://arxiv.org/abs/2209.00645
Autor:
Brena, Camillo, Gigli, Nicola
Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean space. In mo
Externí odkaz:
http://arxiv.org/abs/2206.14864