Related papers: Generalised monopole equations on Kahler surfaces

Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field.…

In this paper, we study the existence of solutions for generalized vector quasi-equilibrium problems. Firstly, we prove that in the case of Banach spaces, the assumptions of continuity over correspondences can be weakened. The theoretical…

We prove the Kobayashi-Hitchin correspondence for parabolic bundles over compact nonK\"{a}hler surfaces with simple normal crossing divisor or compact nonK\"{a}hler manifolds of any dimension with smooth divisor.

In this paper, we show that the cohomology of a general stable bundle on a Hirzebruch surface is determined by the Euler characteristic provided that the first Chern class satisfies necessary intersection conditions. More generally, we…

The Hitchin-Simpson equations are first-order non-linear equations for a pair consisting of a connection and a Higgs field. In this paper, we study the behavior of sequences of solutions to the Hitchin-Simpson equations on closed K\"ahler…

We prove the existence of a Hermitian-Einstein metric on holomorphic vector bundles with a Hermitian metric satisfying the analytic stability condition, under some assumption for the underlying K\"ahler manifolds. We also study the…

This paper aims to investigate the stochastic generalization of the projected deterministic constrained modified Swift-Hohenberg equation. In particular, we prove the global well-posedness and its invariance of Hilbert submanifold i.e. if…

A `coherent system' $(\Cal E,V)$, consists of a holomorphic bundle plus a linear subspace of its space of holomorphic sections. Based on the usual notion in Geometric Invariant Theory, a notion of slope stability has been defined for such…

We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions…

The compactification $\overline M_{1,3}$ of the Gieseker moduli space of surfaces of general type with $K_X^2 =1 $ and $\chi(X)=3$ in the moduli space of stable surfaces parametrises so-called stable I-surfaces. We classify all such…

We establish various stability results for solutions of complex Monge-Amp\`ere equations in big cohomology classes, generalizing results that were known to hold in the context of K\"ahler classes.

The present article is concerned with mirror symmetry for generalized K3 surfaces, with particular emphasis on complex and K\"ahler rigid structures. Inspired by the works of Dolgachev, Aspinwall-Morrison and Huybrechts, we introduce a…

In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a…

We study the Cauchy problem for a generalized derivative nonlinear Schr\"odinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces $H^1$ and $H^2$. Solutions are constructed…

The behaviour of magnetic monopole solutions of the Einstein-Yang-Mills-Higgs equations subject to linear spherically symmetric perturbations is studied. Using Jacobi's criterion some of the monopoles are shown to be unstable. Furthermore…

In this paper we give classification of K\"ahler surfaces of generalized Calabi type.

We construct Bridgeland stability conditions on the the following hyper-K\"ahler or strict Calabi--Yau manifolds: - Generalized Kummer varieties associated to an abelian surface that is isogenous to a product of elliptic curves. - Universal…

In this paper, we study the moduli space of Higgs pairs, which can be considered as a generalization of holomorphic pairs. Higgs pairs are an example of quiver bundles. We introduce the notion of $\tau$-stability of Higgs pairs for…

We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…

We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresponding to the polarization.