General Relativity & Geometric Analysis Seminar, Spring 2008
WEDNESDAY 3:00 to 4:00 PM, Room 4-261.
Talks.
April 23: Nicos Kapuleas (Brown University).
- Title: "Doubling and desingularization constructions for minimal
surfaces".
- Abstract: I will first describe the general idea of a doubling construction:
Given a minimal surface, minimal surfaces are to be constructed,
consisting of two nearby copies of the original surface
joined by many small catenoidal bridges.
In joint work with S. D. Yang we carry such a construction when the
original minimal surface is the Clifford torus in the round
three-sphere.
Using balancing considerations we also establish heuristically
a necessary condition for a general such construction.
I will then describe a general desingularization construction
where the curves of intersection of given minimal surfaces
are replaced by snall handles modeled after Scherk's simply
periodic
minimal surfaces to produce new nearby minimal surfaces.
As an application of this general theorem I demonstrate how to
combine minimal surfaces produced by the doubling of the Clifford
torus
to produce a large class of embedded closed minimal surfaces in the
round three-sphere by desingularization.
April 30: Yair Minsky (Yale) (TEMPORARILY CANCELED)
- Title and abstract (TBA)