The manipulation of surface homeomorphisms is an important aspect in 3D modeling and surface processing. Every homeomorphic surface map can be considered as a quasiconformal map, with its local non-conformal distortion given by its Beltrami differential. As a generalization of conformal maps, quasiconformal maps are of great interest in mathematical study and real applications. Efficient and ac...

Our goal is to provide a survey of some topics in quasiconformal analysis of current interest. We try to emphasize ideas and leave proofs and technicalities aside. Several easily stated open problems are given. Most of the results are joint work with several coauthors. In particular, we adopt results from the book authored by Anderson-Vamanamurthy-Vuorinen [AVV6]. Part 1. Quasiconformal maps an...

2. A topological classification of the almost periodic homeomorphisms on a closed 2-cell. A homeomorphism A of a metric space (X, p) onto itself is said to be almost periodic on X if €>0 implies that there exists a relatively dense sequence {«¿} of integers such that p(x, A"*'(x)) <e for all xGA and i= ±1, ±2, • • •. A homeomorphism A of the space X onto itself is said to be topologically equiv...