GTA-Seminar: Schmidt -- On Spectral Curves of CMC Annuli of Finite Type in S^3

Speaker: Dr. Martin Schmidt (Mannheim)

Time: Thursday, February 7, 12NOON--1PM

Room: Carslaw 707A

Lunch: after the talk. The reservation at Law Annex Cafe is 1:15PM. 

----------------------------------------------------------

Title: On Spectral Curves of CMC Annuli of Finite Type in S^3

Abstract: We call a cmc immersions of the parabolic annulus into 
S^3 to be of finite type, if it has bounded curvature and constant 
Hopf differential with respect to the coordinate z in C/Z. Such an 
annulus is called Alexandrov embedded, if the immersion extends to 
a complete three manifold, whose boundary is the annulus. It is 
called mean convex, if the mean curvature with respect to the inner 
normal is non-negative. All these annuli are determined by solutions 
of the sinh Gordon equation of finite type. The corresponding set of 
spectral curves is shown to be connected. It turns to be a two-dimensional 
set of spectral curves of genus at most one. The corresponding annuli 
are all surfaces of revolution.

----------------------------------------------------------

Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/