Browsing by Advisor "Pingali, Vamsi Pritham"
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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 ... -
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 ... -
On some canonical metrics on holomorphic vector bundles over Kahler manifolds
This thesis consists of two parts. In the first part, we introduce coupled Kähler- Einstein and Hermitian-Yang-Mills equations. It is shown that these equations have an interpretation in terms of a moment map. We identify ... -
Positivity properties of the deformed Hermitian-Yang--Mills and related equations
In the first part of the talk, we briefly introduce the deformed Hermitian-Yang-Mills (dHYM) equation and discuss a result regarding the solvability of the twisted dHYM equation on compact Kähler three-folds with slightly ...