Mon, 30 Jan 2017
16:00 -
17:00
L4
Stable surfaces with constant mean curvature in 3-manifolds admitting a Killing vector field
Miguel Manzano
(King's College)
Abstract
In this talk we will discuss some properties of Schrödinger operators on parabolic manifolds, and particularize them to study the stability operator of a parabolic surface with constant mean curvature immersed in a 3-manifold that admits a Killing vector field. As an application, we will determine the range of values of H such that some homogeneous 3-manifolds admit complete parabolic stable surfaces with constant mean curvature H. Time permitting, we will also discuss some related area and first-eigenvalue estimates for the stability operator of constant mean curvature graphs in such 3-manifolds.