X-Nico

unusual facts about Ennio De Giorgi



Caccioppoli set

In 1952 Ennio de Giorgi presented his first results, developing the ideas of Caccioppoli, on the definition of the measure of boundaries of sets at the Salzburg Congress of the Austrian Mathematical Society: he obtained this results by using a smoothing operator, analogous to a mollifier, constructed from the Gaussian function, independently proving some results of Caccioppoli.

Enrico Giusti

One of the most famous results of Giusti, is the one obtained with Enrico Bombieri and Ennio De Giorgi, concerning the minimality of Simons' cones, and allowing to disprove the validity of Bernstein's theorem in dimension larger than 8.

Plateau's problem

To solve the extended problem, the theory of perimeters (De Giorgi) for codimension 1 and the theory of rectifiable currents (Federer and Fleming) for higher codimension have been developed.


see also