Quadratic differentials and minimal surfaces in hyperbolic space
John Velling
Brooklyn College, C.U.N.Y.
Wednesday, April 25
2:45-3:45 pm, Room 4419
On each complete minimal surface in three dimensional hyperbolic
space, the second
fundamental form splits into conjugate conformal and anticonformal parts.
As the universal cover of the surface is conformally the disc, we may pull
back the conformal part to the disc. The question to be addressed is
the following: Are there holomorphic quadratic differentials which do not
occur in such a fashion? This is the existence part of a natural
existence/uniqueness question about representing complete minimal surfaces
in three dimensional hyperbolic space.