Download Current Topics in Pure and Computational Complex Analysis by Santosh Joshi, Michael Dorff, Indrajit Lahiri PDF

By Santosh Joshi, Michael Dorff, Indrajit Lahiri

The ebook includes thirteen articles, a few of that are survey articles and others learn papers. Written by way of eminent mathematicians, those articles have been provided on the foreign Workshop on complicated research and Its purposes held at Walchand university of Engineering, Sangli. the entire contributing authors are actively engaged in examine fields regarding the subject of the booklet. The workshop provided a accomplished exposition of the new advancements in geometric features conception, planar harmonic mappings, complete and meromorphic capabilities and their purposes, either theoretical and computational. the hot advancements in complicated research and its functions play an important function in learn in lots of disciplines.

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9(1), 101–105 (1959) 20. : O harmonic diffeomorphisms of the unit disc onto a convex domain. Complex Var. Theory Appl. 48, 175–187 (2003) 21. : Planar harmonic maps with inner and Balschke dilatations. J. London Math. Soc. 56(2), 37–48 (1997) 22. : Local properties of light harmonic mappings. Can. J. Math. 44, 135–153 (1992) 23. : On harmonic quasiconformal mappings. Ann. Acad. Sci. Fenn. Ser. A I Math. 425, 1–10 (1968) 24. : Integral means of univalent harmonic maps. Ann. Univ. Mariae Curie-Sklodwska 50, 155–162 (1996) 25.

Open Problem 1 What is the analogue of the Riemann mapping theorem for harmonic mappings? As a final point in this section, we note that, in analogy to S, we define the classes SH and SHO as follows. 2 Harmonic Univalent Mappings and Minimal Graphs Fig. 3 The image of D under fp Fig. 4 The image of D under Fh Fig. 5 The image of D under fh • • • • Analytic polynomial map: Fp (z) = z − 21 z2 Harmonic polynomial map: fp (z) = z + 21 z2 z Analytic right half-plane map: Fh (z) = 1−z z z Harmonic right half-plane map: fh (z) = Re( 1−z ) + iIm( (1−z) 2) 25 26 Z.

Math. Anal. Appl. 340(1), 721–738 (2008) 26. : Gauss curvature estimates for minimal graphs. Ann. Univ. Mariae Curie-Skodowska Sect. A 65(2), 113–120 (2011) 27. : On starlike and close-to-convex functions. Proc. Lond. Math. Soc. 13(3), 290–304 (1963) 28. : Convolutions in Geometric Function Theory. Presses de l’Universite de Montreal, Montreal (1982) 29. : Harmonic mappings whose dilatations are singular inner functions. 1 Introduction A planar harmonic mapping in the unit disk D = {z : |z| < 1} is a complex-valued harmonic function f (z), defined on D.

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