Geometry Seminar: Brander -- Recent Work on Integrable Surfaces Via the Generalized Weierstrass Representation

Speaker: Dr. David Brander (Technical University of Denmark)

http://davidbrander.org/

Time: Tuesday, August 7, 12(NOON)--1PM

Room: Carslaw 707A

Lunch: after the talk (at Taste at Sydney Uni, i.e. 
"Law School Annex Cafe")

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Title:  Recent Work on Integrable Surfaces Via the 
Generalized Weierstrass Representation

Abstract: the classical Weierstrass representation 
for minimal surfaces has been an important tool in 
their study, both for constructing examples and for 
proving general properties about these surfaces. For 
non-minimal CMC surfaces, a generalized Weierstrass 
representation was given by Dorfmeister, Pedit and 
Wu in the 1990’s.  Analogously to the classical 
Weierstrass representation for minimal surfaces, 
all such surfaces can be represented by  pairs of 
holomorphic functions.  This representation has been 
used to construct new examples of CMC surfaces, such 
as CMC trinoids and generalizationis, but, in general 
the method is much less straightforward to make use 
of compared with the minimal case. This is due to a 
loop group splitting which must be performed in the 
passage from the Weierstrass data to the surface, 
which makes it hard to detect geometric properties 
of the surface in the holomorphic data.

In this talk, I will talk about some recent work on 
solving the generalization of Bjorling’s problem to 
the non-minimal case via the loop group representation. 
Other generalizations, which will be mentioned if 
time permits, include the analogous problem for 
constant negative curvature surfaces and also the 
construction of CMC surfaces in Lorentz 3-space 
with prescribed singularities.

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Web site for Geometry Seminar is at: 

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