Special Year 2018-19: Variational Methods in Geometry

Abstract: We define a relative entropy for two expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same smooth cone at infinity. Adapting work of White and using recent results of Bernstein and Bernstein-Wang, we show that...

Abstract: In 1963 Brill and Lindquist asked where one might find the apparent horizons of charged black holes in geometrostatic manifolds that arise as time symmetric solutions to vacuum Einstein Maxwell constraint equations. These manifolds are...

Abstract: I will first concentrate on doubling gluing constructions for minimal surfaces, including a recent construction for free boundary minimal surfaces in the unit ball (with D. Wiygul: arXiv:1711.00818). I will then discuss the Linearized...

Abstract: We give some existence and non-existence results for minimal annuli in H2xR whose data at infinity are given.

Abstract: I will survey the recent progress on the existence problem for minimal hypersurfaces and then point for some new directions. This is joint work with Fernando Marques.

Abstract: Let M be a manifold with bounded Ricci curvature and which is noncollapsed, i.e. |Rc|v>0. Together with Wenshuai Jiang we prove that there then exists the apriori L^2 curvature estimate \int |Rm|^2 C and L^1 hessian estimate \int |\nabla...

Abstract: In this talk we show that given any regular cone with entropy less than that of round cylinder, all smooth self-expanding solutions of the mean curvature flow that are asymptotic to the cone are in the same isotopy class. This is joint...

Abstract: Consider an area minimizing integral current $T$ which has a smooth boundary $\Gamma$ of multiplicity $1$ in some smooth Riemannian ambient manifold $\Sigma$. If the current has codimension $1$ a famous work of Hardt and Simon gives full...