Browsing Mathematics (MA) by thesis submitted date"2024"
Now showing items 1-11 of 11
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Existence and implications of positively curved metrics on holomorphic vector bundles
This thesis is divided into two parts. In the first part, we study interpolating and uniformly flat hypersurfaces in complex Euclidean space. The study of interpolation and sampling in the Bargmann-Fock spaces on the complex ... -
Geometry of normed linear spaces in light of Birkhoff-James orthogonality
In this thesis, we have tried to understand the geometry of normed spaces in the light of Birkhoff-James orthogonality. Using the first two chapters to give introductory notes and to establish relevant notations and ... -
Holomorphic mappings and Kobayashi geometry of domains
In this thesis, we study certain aspects of the geometry of the Kobayashi (pseudo)distance and the Kobayashi (pseudo)metric for domains in $\mathbb{C}^n$. We focus on the following themes: on the interaction between Kobayashi ... -
Invariants Associated with Complete Nevanlinna-Pick Spaces
The broad aim of this thesis is to study certain tuples of bounded operators that satisfy an operator inequality arising from a complete Nevanlinna-Pick kernel. Specifically, we focus on two invariants of these operator ... -
Maps Between Non-compact Surfaces
This thesis focuses on studying proper maps between two non-compact surfaces with a particular emphasis on the topological rigidity and the Hopfian property. Topological rigidity is the property that every homotopy equivalence ... -
The Momentum Construction Method for Higher Extremal Kähler and Conical Higher cscK Metrics
This thesis consists of two parts. In both the parts we study two new notions of canonical K\"ahler metrics on compact K\"ahler manifolds which were introduced by Pingali, viz. `higher extremal K\"ahler metric' and ... -
The monopole-dimer model and eccentricities for Cartesian product of graphs
This thesis comprises two main parts. The details of the two parts are as follows: The first part of the thesis deals with the monopole-dimer model. The dimer (resp. monomer-dimer) model deals with weighted enumeration of ... -
On existence and regularity of some complex Hessian equations on Kahler and transverse Kahler manifolds
The thesis consists of two parts. In the first part of the thesis, we classify the convergence behaviour of rotationally symmetric solutions to the modified J-flow on the blow-up of the complex projective space at a ... -
On regular subalgebras of symmetrizable Kac-Moody algebras and related combinatorics
In this thesis, we study two aspects of Kac-Moody algebras. One is to understand the subalgebras that can be embedded inside a Kac-Moody algebra as subalgebras generated by real root vectors. The other one is to explicitly ... -
On two complex Hessian equations and convergence of corresponding flows
This thesis consists of three parts. Two important complex Hessian equations are studied on certain compact K\"ahler manifolds from different perspectives. The first one is the {\em J-equation} introduced independently by ... -
Symmetric real-closed subsets of affine Kac-Moody Lie Algebras
In this thesis, we study some important classification problems related to affine Kac--Moody Lie algebras. First, we address the combinatorial problem of classifying symmetric real-closed subsets of affine root systems ...