Keywords
- Minimal Surface
- Concentric Circle
- Extremal Function
- Positive Harmonic Function
- Univalent Harmonic Function
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References
D. Bshouty, N. Hengartner, W. Hengartner, A constructive method for starlike harmonic mappings, Numer. Math. 54 (1988), 167–178.
J. Clunie, T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. AI 9 (1984), 3–25.
R.R. Hall, On an inequality of E. Heinz, J. Analyse Math. 42 (1982/83), 185–198.
E. Heinz, Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl., (1952), 51–56.
W. Hengartner, G. Schober, On the boundary behavior of orientation-preserving harmonic mappings, Complex Variables Theory Appl. 5 (1985), 181–192.
W. Hengartner, G. Schober, Harmonic mappings with given dilatation, J. London Math. Soc. 33 (1986), 473–483.
W. Hengartner, G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1–31.
W. Hengartner, G. Schober, Curvature estimates for some minimal surfaces, in Complex Analysis, Articles Dedicated to Albert Pfluger on the Occasion of His 80th Birthday, J. Hersch and A. Huber Eds., Birkhäuser, 1988, 87–100.
J.C.C. Nitsche, On the module of doubly-connected regions under harmonic mappings, Amer. Math. Monthly 69 (1962), 781–782.
R. Osserman, A Survey of Minimal Surfaces, Dover, 1986.
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© 1990 Springer-Verlag
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Schober, G. (1990). Planar harmonic mappings. In: Ruscheweyh, S., Saff, E.B., Salinas, L.C., Varga, R.S. (eds) Computational Methods and Function Theory. Lecture Notes in Mathematics, vol 1435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087906
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DOI: https://doi.org/10.1007/BFb0087906
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