摘要:

This is a survey article on domain constants related to uniform perfectness. We gather comparison theorems for various domain constants, most of which are more or less known or elementary but not stated quantitatively in the literature, and some are new or improved results. Among these theorems, our main result is a comparison of the modulus and the injectivity radius of a hyperbolic Riemann surface. Its proof relies upon a comparison of extremal and hyperbolic lengths, which seems to be interesting in itself. And we include a lower estimate of the Hausdorff dimension of a compact set in the Riemann sphere by the modulus of its complement. We also discuss the variance of these domain constants under conformal, quasiconformal or Möbius maps.

ISSN:0278-1077    

DOI:10.1080/17476939808815116

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

This paper describes the infinite iteration of the Berezin transformBfwhenfbelongs to theLpspace in the polydisc with respect to the invariant measure. When, we get. Whenf∈L1,lim Bn:fexists only whenand the limit is 0. Whenf∈L∞, limBnexists if and only iff=h+gfor somen-harmonichand

ISSN:0278-1077    

DOI:10.1080/17476939808815117

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

For a real smooth hypersurfaceMofCn, we give a subaveraging estimate in some points ofMfor CRfunctions defined near these points. We obtain this by establishing subesti-mates at some point which lies outside ofMand whose normal projection onMis a point of finite type. Secondly, we study the equivalence between the extension of CR functions and the existence of analytic discs.

ISSN:0278-1077    

DOI:10.1080/17476939808815118

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We study distortion of two-dimensional hyperbolic area under quasiconformal mappings,and exhibit “explodable” sets: the image of a set of finite area may have infinite area.

ISSN:0278-1077    

DOI:10.1080/17476939808815119

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

The equation for Gaussian curvature of a conformal metric is a special case of the classical differential equation. δu=f(u) for u ∈C2(ω), where ω⊂R2. We will use a technique introduced by Carleman to find restrictions onfand the set where a subharmonic functionucan satisfy the above equation. This result will generate a relationship between the curvature and the metric of a nonpositively curved surface.

ISSN:0278-1077    

DOI:10.1080/17476939808815120

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor