Renato Caccioppoli and geometric measure theory (Q1315149)

The author's study represents another contribution to the generous initiative of making better known to the world of science the impressive personality of Renato Caccioppoli. The author makes mention of the Congress of the Italian Mathematical Union, held in Taormina, in 1951, and of the new ideas Caccioppoli put forward on that occasion, regarding a new general theory of a \(k\)-dimensional integration in an \(n\)- dimensional space representing a definite extension of the integral theorems in differential forms (the Gauss-Stoke formulae). Also in Taormina, Caccioppoli criticised the directions along which the development of science was advancing. Interesting considerations are also made on the ideas of De Giorgi, as to Caccioppoli's demonstrations.