We compare the topology and deep structure of alternative scale space representations, so called α-scale spaces, 1/2 ≤ α ≤ 1, which are subject to a first order pseudo partial differential equation on the upper half plane {(x, s) ∈ R × R | s > 0}. In particular, the cases α = 1 and α = 1/2, which correspond to respectively Poisson scale space and Gaussian scale space, are considered. Poisson sc...

In his important paper "Coverings of p-adic symmetric regions" [Dr], Drinfeld showed that the p-adic upper half plane and its higher dimensional analogues serve as moduli spaces for certain rigidified formal groups with quaternionic multiplications. Given a formal group of the proper type, together with rigidifying data, over, say, a ring R on which p is nilpotent, Drinfeld constructs an R-valu...

We show that for any K -quasiconformal map of the upper half plane to itself and any ε > 0 , there is a (K + ε) -quasiconformal map of the half plane with the same boundary values which is also biLipschitz with respect to the hyperbolic metric.

The recently introduced SLE growth processes are based on conformal maps from an open and simply-connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions mapping open and simply-connected subsets of smaller and smaller fractions of the upper half-plane to these fractions themselves. The evolutions are all driven by...