To compare and integrate brain data, data from multiple subjects are typically mapped into a canonical space. One method to do this is to conformally map cortical surfaces to the sphere. It is well known that any genus zero Riemann surface can be conformally mapped to a sphere. Therefore, conformal mapping offers a convenient method to parameterize cortical surfaces without angular distortion, ...

The term “complex analysis” refers to the calculus of complex-valued functions f(z) depending on a single complex variable z. To the novice, it may seem that this subject should merely be a simple reworking of standard real variable theory that you learned in first year calculus. However, this näıve first impression could not be further from the truth! Complex analysis is the culmination of a d...

Given any ǫ > 0 and any planar region Ω bounded by a simple n-gon P we construct a (1 + ǫ)-quasiconformal map between Ω and the unit disk in time C(ǫ)n. One can take C(ǫ) = C + C log 1 ǫ log log 1 ǫ . Date: August 13, 2009. 1991 Mathematics Subject Classification. Primary: 30C35, Secondary: 30C85, 30C62 .

To compare and integrate brain data, data from multiple subjects are typically mapped into a canonical space. One method to do this is to conformally map cortical surfaces to the sphere. It is well known that any genus zero Riemann surface can be mapped conformally to a sphere. Since the cortical surface of the brain is a genus zero surface, conformal mapping offers a convenient method to param...