Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 565-580
University of Montenegro, Faculty of Natural Sciences and Mathematics
Cetinjski put b.b., 81000 Podgorica, Montenegro; davidk 'at' ac.me
University of Montenegro, Faculty of Natural Sciences and Mathematics
Cetinjski put b.b., 81000 Podgorica, Montenegro; marijanmmarkovic 'at' gmail.com
University of Belgrade, Faculty of Mathematics
Studentski trg 16, 11000 Belgrade, Serbia;
miodrag 'at' matf.bg.ac.rs
Abstract. We prove representation theorems, the versions of Smirnov's theorem and Carathéodory type theorem for harmonic homeomorphisms of the unit disk onto Jordan surfaces with rectifiable boundaries. Further we establish the classical isoperimetric inequality and the Riesz-Zygmund inequality for Jordan harmonic surfaces without any smoothness assumptions on the boundary.
2010 Mathematics Subject Classification: Primary 30C55; Secondary 31C05.
Key words: Harmonic mappings, harmonic surfaces, isoperimetric inequality.
Reference to this article: D. Kalaj, M. Markovic and M. Mateljevic: Carathéodory and Smirnov type theorems for harmonic mappings of the unit disk onto surfaces. Ann. Acad. Sci. Fenn. Math. 38 (2013), 565-580.
doi:10.5186/aasfm.2013.3822
Copyright © 2013 by Academia Scientiarum Fennica