
Undergraduate Research at GANG
Summer 2000

The
Research Experience for Undergraduate
(REU)
program
is an NSFsupported opportunity for undergraduates to
participate in scientific research.
The geometry and analysisoriented topics for Summer 2000
at the
Center for Geometry, Analysis, Numerics and Graphics
(GANG) include:
 Curves and immersions
 Threedimensional discrete conformal geometry
 Twodimensional stochastic heat flow.
The problem:
How many ways does a curve in the plane bound an immersed surface?
More precisely, given an immersion
f:S^{1}>
R^{2},
of the circle into the plane,
how many ways does
f extend to an immersion
F:M>
R^{2}
of a 2manifold
M?

The solution:
 Illustrations and Animations:
 Research Report: algorithms, proofs and examples
postscript

Software:
a C++ implementation of the algorithm

This problem arises in the classification of Alexandrovembedded
genuszero minimal surfaces in
R^{3}
with finite total curvature and horizontal catenoid ends
(C. Cosin, A. Ros. preprint).
ThreeDimensional Discrete Conformal Maps:

