By Santosh Joshi, Michael Dorff, Indrajit Lahiri

ISBN-10: 8132221125

ISBN-13: 9788132221128

ISBN-10: 8132221133

ISBN-13: 9788132221135

The ebook comprises thirteen articles, a few of that are survey articles and others examine papers. Written by means of eminent mathematicians, those articles have been offered on the overseas Workshop on complicated research and Its purposes held at Walchand collage of Engineering, Sangli. the entire contributing authors are actively engaged in learn fields relating to the subject of the booklet. The workshop provided a entire exposition of the hot advancements in geometric features idea, planar harmonic mappings, whole and meromorphic capabilities and their functions, either theoretical and computational. the hot advancements in complicated research and its functions play a very important position in learn in lots of disciplines.

**Read Online or Download Current Topics in Pure and Computational Complex Analysis PDF**

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**Current Topics in Pure and Computational Complex Analysis - download pdf or read online**

The e-book includes thirteen articles, a few of that are survey articles and others study papers. Written through eminent mathematicians, those articles have been offered on the foreign Workshop on complicated research and Its functions held at Walchand collage of Engineering, Sangli. the entire contributing authors are actively engaged in learn fields with regards to the subject of the e-book.

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**Extra resources for Current Topics in Pure and Computational Complex Analysis**

**Example text**

9 The MinSurfTool applet We can apply the above theorems to planar harmonic mappings. First, recall f = h + g = Re(h + g) + iIm(h − g). 2, choose ϕ1 = h + g and ϕ2 = −i(h − g ). Then we find ϕ3 that will satisfy the requirements of the Weierstrass representation. That is, 0 = (ϕ1 )2 + (ϕ2 )2 + (ϕ3 )2 = h +g 2 2 + −i(h − g ) + (φ3 )2 . √ Solving for ϕ3 √ yields (ϕ3 )2 = −4h g , so ϕ3 = −2i h g . Notice that h g may not always exist as an analytic function, √ √ but whenever it does, the Weierstrass representation applies.

14 Images of the unit disk under f = hn + g n n=4 ϕ = π2 n=4 ϕ = π3 n=4 ϕ = π6 n=4 ϕ= 0 convex domain, Krust theorem guarantees that the conjugate surfaces Y are embedded. These conjugate surfaces Y are Scherk surfaces with higher dihedral symmetry and this establishes the inequality. Open Problem 14 Use theorems and properties about harmonic univalent mappings to prove results about minimal surfaces. 5 Using Harmonic Maps to Construct New Minimal Surfaces In this section we show an example in which a harmonic univalent function is lifted to form a minimal graph that appears to be new.

Sem. 3, 1–118 (1935) 15. : Mapping by p-regular functions. Duke Math. J. 18, 185–210 (1951) 16. : Uniqueness for by p-regular mapping. Duke Math. J. 19, 435–444 (1952) 17. : On the boundary behavior of orientation-preserving harmonic mappings. Complex Var. Theory Appl. 5, 197–208 (1986) 18. : Harmonic mappings with given dilatation. J. Lon. Math. Soc. 33(2), 473–483 (1986) 19. : On one-to-one harmonic mappings. Pac. J. Math. 9(1), 101–105 (1959) 20. : O harmonic diffeomorphisms of the unit disc onto a convex domain.

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

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