Domain Constants And The Geometry Of Teichmùller Spaces

This thesis consists of three parts.In the first part,we give the inner radius of univalency for fan-shaped domains and for quadrilateral domains with vertexes on a circumference and sides forming the sequence abba . Also we estimate the inner radius of univalency for rectangles.In the second part,we introduce and discuss a new domain constant,the pseudo-hyperbolic radius of starlikeness. We also give some properties of some existing domain constants under the change of quasiconformal mappings.In the third part,we will discuss the Banach space Q(X) of all holomorphic quadratic differentials on a hyperbolic Riemann surface X with finite L1 - norm. We discuss the continuity of the mappingdefined by = and also of the inverse mapping V-l .Particularly,we will show that the Teichmullerco-metric on the Teichmuller space is nowhere C1 whenever X is of infinite type,which contains a negative answer to a problem of Gardiner ([Ga],P. 190).Liu Xiao-yi (Complex Analysis) Directed by Prof. Shen Yu-liang...