Quasiconformal harmonic mappings between two doubly connected domains in\n the plane

2021/02/17 by David Kalaj, Kalaj, David
Mathematics · Computer Science · Engineering · #Analytic and geometric function theory #Advanced Mathematical Modeling in Engineering #Elasticity and Wave Propagation

paper · pdf · doi:10.48550/arxiv.2102.08648

Abstract

It is known for some time that there exists an energy-minimal diffeomorphism\nbetween two doubly-connected domains \Ω and D provided that\n\Mod(\Ω)\≤ \ModD and that diffeomorphism is harmonic\n citetedi. In this note we give a short proof of the fact that for given\nannuli \Ω and D satisfying the condition \Mod(\Ω)\≤\n\Mod(D) there exist a K-quasiconformal harmonic diffeomorphism\nf:\Ω onto D, where K=K(\τ), \τ=\Mod(\Ω)/\n\Mod(D) and \lim_{\τ\→ 1}K(\τ)=1.\n

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