Surfaces of constant mean curvature in \Bbb R^3

Surfaces with non-zero constant mean curvature in \Bbb R^3 (``CMC surfaces'') have been a central topic of study in both classical and modern differential geometry. The first part of this talk will be a brief introduction to CMC surfaces.

We will then describe recent joint work with Rafe Mazzeo and Frank Pacard which establishes a general gluing construction for CMC surfaces. This allows one to glue together CMC surfaces provided a natural nondegeneracy condition is satisfied. The method of proof is to study certain boundary value problems for the mean curvature operator.

We will give an explanation of the construction and its application to the existence of both compact CMC surfaces with boundary and noncompact, embedded CMC surfaces.

Refreshments will be served in Math Annex Room 1115, 3:15 p.m.