Conformal Mapping And Its Applications

Abstract

Complex Analysis And Conformal Mapping Play A Central Role In

Mathematical Sciences And Theoretical Physics. The Traditional

Applications Include Differential Equations, Harmonic Analysis,

Potential Theory And Fluid Mechanics. Of Particular Interest To This

Study Is The Complexfied Minkowski Space And Its Corresponding Spin

Space Model Which Is Appropriate For The Description Of Quantum Field

Theory. Moreover, For An Ambitious Scheme To Incorporate

Gravitational Field In A Quantized Form, We Introduced The Threedimensional Complex Projective Space As An Advanced Model Whereby Points Of The Complexified Minkowski Space Are Not Prime But Secondary. In The Light Of Penrose Correspondence These Points Are

Complex Lines In Twistor Space. It Has Been Shown That The

Conformally Invariant Zero-Rest Mass Fields, Such As Weak

Gravitational Field, Are Represented By Contour Integrals Of Holomorphic Functions On Twistor Space.