Moduli of Doubly Connected Domains Under Univalent Harmonic Maps

TY - JOUR

T1 - Moduli of Doubly Connected Domains Under Univalent Harmonic Maps

AU - Bshouty, Daoud

AU - Lyzzaik, Abdallah

AU - Rasila, Antti

AU - Vasudevarao, Allu

PY - 2022/2/23

Y1 - 2022/2/23

N2 - Iwaniec et al. (Proc R Soc Edinb 141A:1017–1030, 2011) raised the following problem: For which values s,t,1<s,t<∞, does there exist a harmonic homeomorphism f:T(s)→T(t), where T(.) is a Teichmüller domain? By restricting ourselves to harmonic homeomorphisms symmetric about the real axis, we establish a two-fold purpose: (a) solve this problem by using the theory of extremal length and (b) test Conjecture 1.4 of loc. cit. regarding the moduli of the doubly connected domains related by harmonic homeomorphisms in light of our results. The paper concludes with relevant and interesting questions.

AB - Iwaniec et al. (Proc R Soc Edinb 141A:1017–1030, 2011) raised the following problem: For which values s,t,1<s,t<∞, does there exist a harmonic homeomorphism f:T(s)→T(t), where T(.) is a Teichmüller domain? By restricting ourselves to harmonic homeomorphisms symmetric about the real axis, we establish a two-fold purpose: (a) solve this problem by using the theory of extremal length and (b) test Conjecture 1.4 of loc. cit. regarding the moduli of the doubly connected domains related by harmonic homeomorphisms in light of our results. The paper concludes with relevant and interesting questions.

KW - Univalent harmonic mappings

KW - Analytic dilatation

KW - Modulus of doubly connected domains and affine capacity

KW - Schwarz–Christoffel transformations

U2 - 10.1007/s12220-022-00895-2

DO - 10.1007/s12220-022-00895-2

M3 - 文章

SN - 1050-6926

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

ER -