From the 1 of 4 linked papers with an AI index.
4 papers
Mean curvature and sharp Willmore inequalities in metric spaces
Nicola Gigli, Ivan Yuri Violo
The paper defines a notion of mean curvature for level sets of Sobolev functions in non‑smooth metric spaces with Ricci curvature bounded below, introduces a Willmore functional, a…
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 gen…