1 citations · 1 across the 5 of their papers we have counts for
5 papers
Mean curvature and sharp Willmore inequalities in metric spaces
Nicola Gigli, Ivan Yuri Violo
The goal of this work is to introduce a notion of mean curvature for level sets of functions in non-smooth spaces with Ricci curvature bounded below, and to prove that it satisfies…
Some examples of use of transfinite induction in analysis
Nicola Gigli
It is not uncommon in analysis that existence of extremal objects is obtained via an iterative procedure: we start from a given admissible object, then modify it, then modify again…
Hyperbolic Banach spaces
Nicola Gigli
The standard theory of Banach spaces is built upon the notions of vector space, triangle inequality and Cauchy completeness. Here we propose a `hyperbolic' variant of this `ellipti…
Notes on the Cheeger and Colding version of the Reifenberg theorem for metric spaces
Nicola Gigli, Ivan Yuri Violo
The classical Reifenberg's theorem says that a set which is sufficiently well approximated by planes uniformly at all scales is a topological Hölder manifold. Remarkably, this gene…
A general splitting principle on RCD spaces and applications to spaces with positive spectrum
Nicola Gigli, Fabio Marconi
In this paper we develop a general `analytic' splitting principle for RCD spaces: we show that if there is a function with suitable Laplacian and Hessian, then the space is (isomor…