摘要:

LetXandYbe hyperbolic Riemann surfaces andf:X→Ya conformal mapping ofXintoY. Suppose γ is a smooth path onXaεγ andkx(a, γ)(kγ(f(a)fеγ)) denotes the hyperbolic curvature of γ(fеγ) ata(f(a)). We investigate the comparison ofkx(a,γ) andky:(f(a),γ); this is a continuation of the work of Flinn and Osgood who considered the case in whichXandyare simply connected. We prove the monotonicity property thatky(f(a),f,y)≤kx:(a,γ) provided thatkx(a,γ)≤2 and the induced homomorphismf*. φ(X,a) →φ(yf(a)) of the fundamental groups is injective. WhenXis simply connected, this condition onf*is automatically satisfied. Also, ifXandYare simply connected, we show that the monotonicity property actually holds forkx(a,γ)≤1 wheneverf(X) is a hyperbolicallv 1-convex subset ofY.

ISSN:0278-1077    

DOI:10.1080/17476938908814347

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938908814348

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938908814349

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

We find sharp coefficient bounds for the inverses of functions of the formthat satisfy. We also solve the inverse coefficient problem in the casesn= 2, 3, 4 for such functions that are starlike of order α 0 ≤α≤1, and conjecture the correct bounds for alln.

ISSN:0278-1077    

DOI:10.1080/17476938908814350

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

Letfghbe real functions on the unit circle, and letf0g0h0denote their symmetric decreasing rearrangements. We prove, under appropriate integrability assumptions, the inequality.

ISSN:0278-1077    

DOI:10.1080/17476938908814351

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

LetGbe a disk or half plane and letfbe analytic inGand continuous in Ǥ, the closure ofG. Letz1be a fixed boundary point ofGand suppose thatfor allzon the boundary ofGwhere μ is a suitable type of function. We determine the best constantCin various situations such that thenfor allzinǤ. All these constantsCare less than 2.2. WhenGis a half planefmust satisfy a growth condition.

ISSN:0278-1077    

DOI:10.1080/17476938908814352

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

Letfbe a real, continuous function on the circle groupT. Then there is a homeomorphism g ofTonto itself such that the function conjugate tois continuous and of bounded variation onT. This is obtained as a consequence of an analogous result for the Hilbert transform.

ISSN:0278-1077    

DOI:10.1080/17476938908814353

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938908814354

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

We give a slightly different proof of a theorem by N, Steinmetz: Suppose thatfis a transcendental meromorphic function Then for ε > 0 and distinct functions a1...aqsuch that T(r. aj) = 0(T(r,f) we haveFor the proof we use a lemma on the zeros of linear differential polynomials of the form W(a1…aq,f).

ISSN:0278-1077    

DOI:10.1080/17476938908814355

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938908814356

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor