arXiv subjects

Vamsi Pritham Pingali

Publications and source records attributed to Vamsi Pritham Pingali.

22 records · Page 2Linked to original sources

arXiv2017

Quillen metrics and perturbed equations

We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations - the generalised Monge-Amp`ere equation, the almost Hitchin system, and the Calabi-Yang-Mills equations. These are all perturbations of already existing equations. Our construction for the generalised Monge-Amp`ere equation is conditioned on a conjecture from algebraic geometry. In addition, we prove that for small values of the perturbation parameters, some of these equations have solutions.

math-ph↗

arXiv2017

A note on higher extremal metrics

In this paper we introduce higher extremal Kahler metrics. We provide an example of the same on a minimal ruled surface. We also prove a perturbation result that implies that there are non-trivial examples of higher constant scalar curvature metrics, which are basically metrics where the top Chern form is harmonic. We also give a relatively short proof of a formula due to Liu for the Bando-Futaki invariants (which are obstructions for the existence of harmonic Chern forms) of hypersurfaces in projective space.

math.DG↗

arXiv2017

Existence of coupled Kähler-Einstein metrics using the continuity method

In this paper we prove the existence of coupled Kähler-Einstein metrics on complex manifolds whose canonical bundle is ample. These metrics were introduced and their existence in the said case was proven by Hultgren and Nyström using calculus of variations. We prove the result using the method of continuity. In the process of proving estimates, akin to the usual Kähler-Einstein metrics, we reduce existence in the Fano case to a C^0 estimate.

math.DG↗

arXiv2017

Representability of Chern-Weil forms

In this paper we look at two naturally occurring situations where the following question arises. When one can find a metric so that a Chern-Weil form can be represented by a given form ? The first setting is semi-stable Hartshorne-ample vector bundles on complex surfaces where we provide evidence for a conjecture of Griffiths by producing metrics whose Chern forms are positive. The second scenario deals with a particular rank-2 bundle (related to the vortex equations) over a product of a Riemann surface and the sphere.

math.DG↗