Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Violo, Ivan Yuri"'
Autor:
Nobili, Francesco, Violo, Ivan Yuri
We study fine P\'olya-Szeg\H{o} rearrangement inequalities into weighted intervals for Sobolev functions and functions of bounded variation defined on metric measure spaces supporting an isoperimetric inequality. We then specialize this theory to spa
Externí odkaz:
http://arxiv.org/abs/2409.14182
Autor:
Gigli, Nicola, Violo, Ivan Yuri
The classical Reifenberg's theorem says that a set which is sufficiently well approximated by planes uniformly at all scales is a topological H\"older manifold. Remarkably, this generalizes to metric spaces, where the approximation by planes is repla
Externí odkaz:
http://arxiv.org/abs/2406.13771
We prove that Ahlfors-regular RCD spaces are uniformly rectifiable. The same is shown for Ahlfors regular boundaries of non-collapsed RCD spaces. As an application we deduce a type of quantitative differentiation for Lipschitz functions on these spac
Externí odkaz:
http://arxiv.org/abs/2311.09907
Autor:
Fässler, Katrin, Violo, Ivan Yuri
We introduce new flatness coefficients, which we call \emph{$\iota$-numbers}, for Ahlfors regular sets in metric spaces. We investigate the relation between Carleson-type geometric lemmas for $\iota$-numbers and other concepts related to quantitative
Externí odkaz:
http://arxiv.org/abs/2310.10519
We prove the Pleijel theorem in non-collapsed RCD spaces, providing an asymptotic upper bound on the number of nodal domains of Laplacian eigenfunctions. As a consequence, we obtain that the Courant nodal domain theorem holds except at most for a fin
Externí odkaz:
http://arxiv.org/abs/2307.13983
Autor:
Violo, Ivan Yuri
In 1964 A. Bruckner observed that any bounded open set in the plane has an inscribed triangle, that is a triangle contained in the open set and with the vertices lying on the boundary. We prove that this triangle can be taken uniformly fat, more prec
Externí odkaz:
http://arxiv.org/abs/2306.07571
We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of sets under perturbations with balls. More precisely, we prove that iso
Externí odkaz:
http://arxiv.org/abs/2303.01280
Autor:
Nobili, Francesco, Violo, Ivan Yuri
We study the qualitative stability of two classes of Sobolev inequalities on Riemannian manifolds. In the case of positive Ricci curvature, we prove that an almost extremal function for the sharp Sobolev inequality is close to an extremal function of
Externí odkaz:
http://arxiv.org/abs/2210.00636
Autor:
Nobili, Francesco, Violo, Ivan Yuri
We prove that if $M$ is a closed $n$-dimensional Riemannian manifold, $n \ge 3$, with ${\rm Ric}\ge n-1$ and for which the optimal constant in the critical Sobolev inequality equals the one of the $n$-dimensional sphere $\mathbb{S}^n$, then $M$ is is
Externí odkaz:
http://arxiv.org/abs/2108.02135
