GeoTop Geometry Day - November 2023

13:00-13:15:

Arrival (tea/coffee) [Room 04.4.19]

13:15-14:15:

Speaker: Franco Vargas Pallete (Yale) [Room: Aud 09, HCØ]

Title: Isoperimetric profile comparison for convex co-compact hyperbolic 3-manifolds

Abstract: Convex co-compact hyperbolic 3-manifolds are the generic infinite volume hyperbolic 3-manifolds with finitely generated fundamental group, while an isoperimetric profile is a function that describes the smallest perimeter to bound a region of a given volume. Using results of renormalized volume (which is a renormalization of the infinite volume) we will show a comparison and rigidity for isoperimetric profiles of convex co-compact hyperbolic 3-maniffolds and their model hyperbolic geometry. We will use this comparison and rigidity to prove a comparison and rigidity result for the Cheeger constant (optimal perimeter/volume ratio) on a class of convex co-compact manifolds. We will show that the Cheeger constant attains its maximum value on Fuchsian manifolds. This is based on joint works with Celso Viana.

14:15-15:15:

Tea/coffee/cookies [Room 04.4.19]

15:15-16:15:

Speaker: Shengwen Wang (Queen Mary U) [Room: Aud 09]

Title: Phase transitions with Allen-Cahn mean curvature bounded in L^p.

Abstract: We consider the varifolds associated to a phase transition problem whose first variation of Allen-Cahn energy is L^p integrable with respect to the energy measure. We can see that the Dirichlet and potential part of the energy are almost equidistributed. After passing to the phase field limit, one can obtain an integer rectifiable varifold with bounded L^p mean curvature. This is joint work with Huy Nguyen.