The Hitchin--Kobayashi Correspondence for Quiver Bundles over Generalized K\"ahler Manifolds

In this paper, we establish the Hitchin--Kobayashi correspondence for the $I_\pm$-holomorphic quiver bundle $\mathcal{E}=(E,\phi)$ over a compact generalized K\"{a}hler manifold $(X, I_+,I_-,g, b)$ such that $g$ is Gauduchon with respect to both $I_+$ and $I_-$, namely $\mathcal{E}$ is $(\alpha,\sigma,\tau)$-polystable if and only if $\mathcal{E}$ admits an $(\alpha,\sigma,\tau)$-Hermitian--Einstein metric.Comment: To appear in The Journal of Geometric Analysi

Flat λ\lambda-Connections, Mochizuki Correspondence and Twistor Spaces

In this paper, we first collect some basic results for $\lambda$-flat bundles, and then get an estimate for the norm of $\lambda$-flat sections, which leads to some vanishing theorem. Mochizuki correspondence provides a homeomorphism between the moduli space of (poly-)stable $\lambda$-flat bundles and that of (poly-)stable Higgs bundles, and provides a dynamical system on the later moduli space (the Dolbeault moduli space). We investigate such dynamical system, in particular, we discuss the corresponding first variation and asymptotic behavior. We generalize the Deligne's twistor construction for any element $\gamma$ of the outer automorphism group of the fundamental group of Riemann surface to obtain the $\gamma$-twistor space, and we apply the twistor theory to study a Lagrangian submanifold of the de Rham moduli space. As an application, we prove a Torelli-type theorem for the twistor spaces, and meanwhile, we prove that the oper stratum in the oper stratification of the de Rham moduli space is the unique closed stratum of minimal dimension, which partially confirms a conjecture by Simpson.Comment: Simpson pointed out a mistake on the Moishezon property for the twistor space in the last version, we delete it and add a section on the study of oper stratification of the de Rham moduli space as an applicatio

Negative phase velocity in nonlinear oscillatory systems --mechanism and parameter distributions

Waves propagating inwardly to the wave source are called antiwaves which have negative phase velocity. In this paper the phenomenon of negative phase velocity in oscillatory systems is studied on the basis of periodically paced complex Ginzbug-Laundau equation (CGLE). We figure out a clear physical picture on the negative phase velocity of these pacing induced waves. This picture tells us that the competition between the frequency $\omega_{out}$ of the pacing induced waves with the natural frequency $\omega_{0}$ of the oscillatory medium is the key point responsible for the emergence of negative phase velocity and the corresponding antiwaves. $\omega_{out}\omega_{0}>0$ and $|\omega_{out}|<|\omega_{0}|$ are the criterions for the waves with negative phase velocity. This criterion is general for one and high dimensional CGLE and for general oscillatory models. Our understanding of antiwaves predicts that no antispirals and waves with negative phase velocity can be observed in excitable media