Abstract: I will go over some recent work that I have been
involved in on surface geometry in complete locally homogeneous
3-manifolds X. In joint work with Mira, Perez and Ros, we have been
able to finish a long term project related to the Hopf...
Abstract: We will explain how to prove properness of a complete
embedded minimal surface in Euclidean three-space, provided that
the surface has finite genus and countably many limit ends (and
possibly compact boundary).
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).
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.
