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).
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: 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...
