Extreme points and support points of families of harmonic Bloch mappings

关于一类映射的均匀轻度性及柯比-布洛赫定理

On uniformly lightness of one class of mappings and Koebe-Bloch theorem

研究一类满足路径模数扭曲估计的映射，证明其均匀轻度性，并在更严格条件下给出连续体直径扭曲的显式估计。

Normal families and quasiregular mappings

Beardon and Minda gave a characterization of normal families of holomorphic and meromorphic functions in terms of a locally uniform Lipschitz condition. Here, we generalize this viewpoint to families of mappings in higher dimensions that are locally uniformly continuous with respect to a given modulus of continuity. Our main application is to the normality of families of quasiregular mappings through a locally uniform Hölder condition. This provides a unified framework in which to consider families of quasiregular mappings, both recovering known results of Miniowitz, Vuorinen and others, and y…

Extreme points and saturated polynomials

We consider the problem of characterizing the extreme points of the set of analytic functions f on the bidisk with positive real part and f(0)=1. If one restricts to those f whose Cayley transform is a rational inner function, one gets a more tractable problem. We construct families of such f that are extreme points and conjecture that these are all such extreme points. These extreme points are constructed from polynomials dubbed saturated, which roughly speaking means they have no zeros in the bidisk and as many zeros as possible on the boundary without having infinitely many zeros.