• Analytic Continuation In Several Complex Variables 

      Biswas, Chandan (2014-06-30)
      We wish to study those domains in Cn,for n ≥ 2, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We demonstrate that this study ...
    • Exploring Polynomial Convexity Of Certain Classes Of Sets 

      Gorai, Sushil (2011-07-18)
      Let K be a compact subset of Cn . The polynomially convex hull of K is defined as The compact set K is said to be polynomially convex if = K. A closed subset is said to be locally polynomially convex at if there ...
    • On the Kobayashi geometry of domains 

      Maitra, Anwoy
      In this thesis we study questions broadly related to the Kobayashi (pseudo)distance and (pseudo)metric on domains in ℂn. Specifically, we study the following subjects: Estimates for holomorphic images of subsets in convex ...
    • On The Structure of Proper Holomorphic Mappings 

      Jaikrishnan, J (2017-09-28)
      The aim of this dissertation is to give explicit descriptions of the set of proper holomorphic mappings between two complex manifolds with reasonable restrictions on the domain and target spaces. Without any restrictions, ...
    • The Pick-Nevanlinna Interpolation Problem : Complex-analytic Methods in Special Domains 

      Chandel, Vikramjeet Singh (2018-06-13)
      The Pick–Nevanlinna interpolation problem, in its fullest generality, is as follows: Given domains D1, D2 in complex Euclidean spaces, and a set f¹ zi; wiº : 1 i N g D1 D2, where zi are distinct and N 2 š+, N 2, find ...
    • Some Descriptions Of The Envelopes Of Holomorphy Of Domains in Cn 

      Gupta, Purvi (2011-08-09)
      It is well known that there exist domains Ω in Cn,n ≥ 2, such that all holomorphic functions in Ω continue analytically beyond the boundary. We wish to study this remarkable phenomenon. The first chapter seeks to motivate ...