Annales Academiĉ Scientiarum Fennicĉ
Mathematica
Volumen 38, 2013, 595-616

JOHN SURFACES ASSOCIATED WITH A CLASS OF HARMONIC MAPPINGS

Willy Sierra

Universidad del Cauca, Departamento de Matemáticas
Popayán, Colombia; wsierra 'at' unicauca.edu.co

Abstract. We study some criteria for the image of the unit disk under the canonical lift ~f of a harmonic mapping f to be a John surface and a linearly connected surface. Growth results of the metric of the minimal surface associated to ~f are obtained. Some our results generalize known ones in geometric functions theory.

2010 Mathematics Subject Classification: Primary 30C55; Secondary 31A05, 53A10, 30C45.

Key words: Schwarzian derivative, John surface, harmonic mapping, minimal surface.

Reference to this article: W. Sierra: John surfaces associated with a class of harmonic mappings. Ann. Acad. Sci. Fenn. Math. 38 (2013), 595-616.

Full document as PDF file

doi:10.5186/aasfm.2013.3844

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