# Workshop on Mean Curvature and Regularity

Various

### Progress in the theory of CMC surfaces in locally homgeneous 3-manifolds X

William Meeks

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...

### The embedded Calabi-Yau problem for minimal surfaces of finite genus

Joaquin Perez

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).

This is joint work with...

### Generic uniqueness of expanders with vanishing relative entropy

Felix Schulze

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...

### Locating Minimal Surfaces in Geometrostatic Manifolds

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...

### Recent gluing constructions in Geometry and the gluing methodology

Nicos Kapouleas

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...

### Sinh-Gordon equation and application to the geometry of CMC surfaces.

Laurent Hauswirth

### A Plateau problem at infinity in H2xR

Magdalena Rodriguez

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

### Progress on existence of minimal surfaces

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.