## Edoardo Cavallotto

Ph.D. student @ Université Paris-Sud (PSUD)

since 10/1/2014 for 3 years.

under the supervision of **Prof. Guy David**

### Research

The subject of my research is the Plateau problem in some of its variants. There are many of them but the general idea is the following: given a boundary set B, one tries to minimize the area of a set E bounded by B. Part of the problem is hidden in the choice of a suitable definition of “area” and “bounded by”. In particular we are interested in a formalisation, similar to the Almgren's one, where the area is the Hausdorff measure and the boundary condition is expressed in terms of a one parameter family of deformation. We are concerned in the existence of minimisers (a property that is still widely unknown both in Almgren's and in size minimizing current framework) as well as in minimiser's (and, in general, almost minimiser's) regularity properties, in particular near the boundary, another question that has not been investigated very much. We also focused on a slight variant of the problem called “sliding boundary”. In this new setting, after fixing a set L, we only consider those modifications f such that f(x) sits in L whenever x belongs to L, and the functional we want to minimise is modified on L by multiplying the Hausdorff area by a parameter 0

### Local training activities:

- Complex geometry and Hodge groups (lecturer L. Charles) - A.A 2014/15 Paris, France
- Differential topology (lecturer A. Zorich) - A.A 2014/15 Paris, France
- Rectifiability and currents (lecturer T. De Pauw) - A.A 2014/15 Paris, France
- Séminaire Périodique d'analyse harmonique d'Orsay - A.A 2014/15 Paris, France

### Network-wide training activities:

- Workshop on Analysis and Geometry in metric spaces - June 1-5, 2015 Madrid, Spain
- Geometric measure theory and calculus of variations - June 15 - July 4, 2015 Grenoble, France

### Outreach:

- Workshop Day Fête de la science à l'Université Paris-Sud - October 7-11, 2015 Paris, France
- Marie Curie Ambassador Analyse Mathématique - A.A 2014/15 Paris, France
- Workshop Day Journée de rentrée - A.A 2014/15 Paris, France

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