A Mathematical Tribute to Ennio De Giorgi
timetable:
Tue 20 Sep, 10:00 - 10:55, Palazzo dei Congressi
<< Go back
Min-max methods for surfaces with boundary
speaker: Camillo De Lellis (Institute for Advanced Study, Princeton)abstract: We extend the min-max constructions pioneered by Pitts to hypersurfaces with a prescribed boundary $\gamma$ on a bounded convex domain, proving full boundary regularity of the min-max hypersurface. One main implication is the following $n$-dimensional version of a classical theorem for $2$-dimensional surfaces: if $\gamma$ bounds two (regular) embedded local minima then it bounds a third distinct embedded minimal hypersurface. The latter is regular up to a compact set of codimension $n-7$ which does not intersect $\gamma$.
timetable:
Tue 20 Sep, 10:00 - 10:55, Palazzo dei Congressi
<< Go back