7 citations · 10 across the 19 of their papers we have counts for
5 papers · 1 filter
Ricci curvature bounded below and uniform rectifiability
Matthew Hyde, Michele Villa, Ivan Yuri Violo
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…
On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 1
Katrin Fässler, Ivan Yuri Violo
We introduce new flatness coefficients, which we call -numbers, for Ahlfors -regular sets in metric spaces (). Using these coefficients for , we charact…
Pleijel nodal domain theorem in non-smooth setting
Nicolò De Ponti, Sara Farinelli, Ivan Yuri Violo
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 obtai…
Fat triangles inscribed in arbitrary planar domains
Ivan Yuri Violo
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 bound…
Topological regularity of isoperimetric sets in PI spaces having a deformation property
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1
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…