Scale Curves in Conformal Maps

Conformal Images of Carleson Curves

We show that if γ is a curve in the unit disk, then arclength on γ is a Carleson measure iff the image of γ has finite length under every conformal map onto a domain with rectifiable boundary. Date: July 27, 2012. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

The Conformal Theory of Curves.

Conformal Maps and Minimal Surfaces

Bifurcation Curves in Discontinuous Maps

Several discrete-time dynamic models are ultimately expressed in the form of iterated piecewise linear functions, in oneor twodimensional spaces. In this paper we study a one-dimensional map made up of three linear pieces which are separated by two discontinuity points, motivated by a dynamic model arising in social sciences. Starting from the bifurcation structure associated with one-dimension...

Stable Maps of Curves

Let h:X → Y be a finite morphism of smooth connected complete curves over Cp. We show h extends to a finite morphism between semi-stable models of X and Y . 2000 Mathematics Subject Classification: 11G20