Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
Abstract The conformal mapping $$f(z)=(z+1)^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> from $${\mathbb {D}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> </mml:math> onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 …