2 papers
math.AP2025
Calibrated Reifenberg With Holes
Susanna Bertolini, Alessandro Preti, Daniele Valtorta
In this article, we study a calibrated version of Reifenberg theorem "with holes". In particular we study sets that are suitably approximable at all points and scales by calibrated…
math.FA2025
A note on smooth rotund norms which are not midpoint locally uniformly rotund
Carlo Alberto De Bernardi, Alessandro Preti, Jacopo Somaglia
We prove that every separable infinite-dimensional Banach space admits a Gâteaux smooth and rotund norm which is not midpoint locally uniformly rotund. Moreover, by using a simila…