6 papers
The coerciveness and generalised Monge-Ampère equations
Gao Chen, Kartick Ghosh, Ziyue Wang
In this paper, we prove the equivalence between coerciveness and the existence of a solution to the generalised Monge-Ampère equations for right-Noetherian polynomials satisfying s…
Geodesics for generalised Monge-Ampère equations
Gao Chen, Kartick Ghosh, Sijie Nie
Xiuxiong Chen proved the existence of geodesics in the space of Kähler potentials and the convexity of the -functional along geodesics. Analogous…
On The Ellipticity of Generalised Monge-Ampère Equations on Vector Bundles
Gao Chen, Kartick Ghosh
In this paper, we study the ellipticity of the vector bundle versions of the Monge-Ampère, , dHYM and -equations at a point. These are nonlinear geometric partial differe…
A formula for the α-Futaki character
Kartick Ghosh
Alvarez-Consul--Garcia-Fernandez--Garcia-Prada introduced the Kähler-Yang-Mills equations. They also introduced the -Futaki character, an analog of the Futaki invariant, as an o…
Coupled Kähler-Einstein and Hermitian-Yang-Mills equations
Kartick Ghosh
We introduce a new system of equations coupling Kähler-Einstein and Hermitian-Yang-Mills equations. We provide a moment map interpretation of these equations. We identify a Futaki…
Vortex-type equations on compact Riemann surfaces
Kartick Ghosh
In this paper, we prove \emph{a priori} estimates for some vortex-type equations on compact Riemann surfaces. As applications, we recover existing estimates for the vortex bundle M…