We will present the project of using the Willmore elastic energy as
a quasi-Morse function to explore the topology of immersions of the
2-sphere into Euclidean spaces and explain how this relates to the
classical theory of complete minimal surfaces...
A translator for mean curvature flow is a hypersurface $M$ with the
property that translation is a mean curvature flow. That is, if the
translation is $t\rightarrow M+t\vec{v}$, then the normal component
of the velocity vector $\vec{v}$ is equal to...
Given a Weinstein domain $M$ and a compactly supported, exact
symplectomorphism $\phi$, one can construct the open symplectic
mapping torus $T_\phi$. Its contact boundary is independent of
$\phi$ and thus $T_\phi$ gives a Weinstein filling of $T_0...
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).
