On harmonic functions and the Schwarz lemma

Kalaj, David; Vuorinen, Matti

doi:10.1090/S0002-9939-2011-10914-6

On harmonic functions and the Schwarz lemma
HTML articles powered by AMS MathViewer

by David Kalaj and Matti Vuorinen PDF

Proc. Amer. Math. Soc. 140 (2012), 161-165 Request permission

Abstract:

We study the Schwarz lemma for harmonic functions and prove sharp versions for the cases of real harmonic functions and the norm of harmonic mappings.

References

Sheldon Axler, Paul Bourdon, and Wade Ramey, Harmonic function theory, Graduate Texts in Mathematics, vol. 137, Springer-Verlag, New York, 1992. MR 1184139, DOI 10.1007/b97238
Peter Duren, Harmonic mappings in the plane, Cambridge Tracts in Mathematics, vol. 156, Cambridge University Press, Cambridge, 2004. MR 2048384, DOI 10.1017/CBO9780511546600
Erhard Heinz, On one-to-one harmonic mappings, Pacific J. Math. 9 (1959), 101–105. MR 104933, DOI 10.2140/pjm.1959.9.101
D. Kalaj, Harmonic functions and harmonic quasiconformal mappings between convex domains, thesis, Beograd, 2002.
Miljan Knežević and Miodrag Mateljević, On the quasi-isometries of harmonic quasiconformal mappings, J. Math. Anal. Appl. 334 (2007), no. 1, 404–413. MR 2332565, DOI 10.1016/j.jmaa.2006.12.069
M. Pavlović, A Schwarz lemma for the modulus of a vector-valued analytic function, Proc. Amer. Math. Soc. 139 (2011), 969–973.
Miroslav Pavlović, Introduction to function spaces on the disk, Posebna Izdanja [Special Editions], vol. 20, Matematički Institut SANU, Belgrade, 2004. MR 2109650
Tom Yau-Heng Wan, Constant mean curvature surface, harmonic maps, and universal Teichmüller space, J. Differential Geom. 35 (1992), no. 3, 643–657. MR 1163452