6 mar 2019
Aula Seminari, Dipartimento di Matematica, Università di Pisa
We study a geometric flow driven by the fractional mean curvature. The notion of fractional mean curvature arises naturally when performing the first variation of the fractional perimeter functional. More precisely, we show the existence of surfaces which develope neckpinch singularities in any dimension $n\ge 2$. Interestingly, in dimension $n = 2$ our result gives a counterexample to Grayson Theorem for the classical mean curvature flow. We also present a very recent result, in the volume preserving case, establishing convergence to a sphere. The results have been obtained in collaboration with C. Sinestrari and E. Valdinoci.