Radial extension of a bi-Lipschitz parametrization of a starlike Jordan\n curve

2010/11/23 by David Kalaj, Kalaj, David
Mathematics · Medicine · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Spine and Intervertebral Disc Pathology

paper · pdf · doi:10.48550/arxiv.1011.5204

openalex publication_date 2010/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discus the radial extension w of a bi-Lipschitz\nparameterization F(e^it)=f(t) of a starlike Jordan curve \γ w.r. to\n0. We show that, if parameterization is bi-Lipschitz, then the extension is\nbi-Lipschitz and consequently quasiconformal. If \γ is the unit circle,\nthen \Lip(f)=\Lip(F)=\Lip(w)=K_w. If \γ is not\na circle centered at origin, and F is a polar parametrization of \γ,\nthen we show that \Lip(f)=\Lip(F)<\Lip(w).\n

Citations

• The boundary correspondence under quasiconformal mappings

Related

• On Quasi-inversions
• Bi-Lipschitz quasiconformal extensions
• A planar bi-Lipschitz extension Theorem
• Radial length, radial John disks and K-quasiconformal harmonic mappings
• Pavlovic's theorem in space