Calculus of Variations and Geometric Measure Theory

Bubbling analysis for free-boundary minimal hypersurfaces

Ben Sharp

created by malchiodi on 16 Jul 2018
modified on 20 Jul 2018

24 jul 2018 -- 14:00   [open in google calendar]

Scuola Normale Superiore, Aula Bianchi


We will discuss some recent results in the analysis of degenerating sequences of free-boundary minimal hypersurfaces (FBMH), with a view to gaining qualitative (and quantitative) relationships between their Morse indices, geometry and topology. A FBMH is a manifold with boundary which is a critical point of the area functional under the sole constraint that its boundary must lie along the boundary of the ambient space. Thus the mean curvature vanishes on the interior and they meet the boundary orthogonally. The Morse index is (roughly speaking) the number of local directions one can push the hypersurface to decrease area. I will present joint works with L. Ambrozio, A. Carlotto and R. Buzano.