Browsing by Advisor "Verma, Kaushal"
Now showing items 110 of 10

Dynamical Properties of Families of Holomorphic Mappings
(20180608)Thesis Abstract In the first part of the thesis, we study some dynamical properties of skew products of H´enon maps of C2 that are fibered over a compact metric space M . The problem reduces to understanding the dynamical ... 
Function Theory On NonCompact Riemann Surfaces
(20140630)The theory of Riemann surfaces is quite old, consequently it is well developed. Riemann surfaces originated in complex analysis as a means of dealing with the problem of multivalued functions. Such multivalued functions ... 
The Green's Function, the Bergman Kernel and Quadrature Domains in Cn
(20180608)In the ﬁrst part of this thesis, we prove two density theorems for quadrature domains in Cn ,n≥2. It is shown that quadrature domains are dense in the class of all product domains of the form D×Ωwhere D⊂Cn−1 is a smoothly ... 
Hermitian Metrics and Singular Riemann Surface Foliations
The main aim of this thesis is to understand curvature properties of a given hermitian metric by restricting it to the leaves of a suitable singular Riemann surface foliation. We will specifically consider the complete ... 
An Introduction to Minimal Surfaces
(20171210)In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform ... 
Rigidity And Regularity Of Holomorphic Mappings
(20150716)We deal with two themes that are illustrative of the rigidity and regularity of holomorphic mappings. The first one concerns the regularity of continuous CR mappings between smooth pseudo convex, finite type hypersurfaces ... 
The Role Of Potential Theory In Complex Dynamics
(20140407)Potential theory is the name given to the broad field of analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, Green’s functions, potentials and capacity. In this text, our main ... 
Shiftlike Automorphisms of Ck
(20180103)We use transcendental shiftlike automorphisms of Ck, k > 2 to construct two examples of nondegenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck, k>2 whose range avoids a ... 
A Study of Some Conformal Metrics and Invariants on Planar Domains
The main aim of this thesis is to explain the behaviour of some conformal metrics and invariants near a smooth boundary point of a domain in the complex plane. We will be interested in the invariants associated to the ... 
A Study Of The Metric Induced By The Robin Function
(20130913)Let D be a smoothly bounded domain in Cn , n> 1. For each point p _ D, we have the Green function G(z, p) associated to the standard sumofsquares Laplacian Δ with pole at p and the Robin constant __ Λ(p) = lim G(z, p) ...