arXiv subjects
Publications and source records attributed to Changpeng Pan.
For any Hermitian holomorphic vector bundle with Nakano positive curvature tensor, Demailly introduced a Monge-Amp\`ere type equation. When the rank of the bundle is $1$, it becomes the usual Monge-Amp\`ere equation. In this paper, we solve this equation in the conformal class of a Nakano positive Hermitian metric.
This paper investigates the generalizations and applications of weakly $p$-K\"ahler hyperbolic manifolds.
In this paper, we study the non-Hermitian Yang-Mills (NHYM for short) bundles over compact Kähler manifolds. We show that the existence of harmonic metrics is equivalent to the semisimplicity of NHYM bundles, which confirms the Conjecture 8.7 in \cite{KV}.
In this paper, we consider the Yang-Mills-Higgs flow for twisted Higgs pairs over Kähler manifolds. We prove that this flow converges to a reflexive twisted Higgs sheaf outside a closed subset of codimension $4$, and the limiting twisted Higgs sheaf is isomorphic to the double dual of the graded twisted Higgs sheaves associated to the Harder-Narasimhan--eshadri filtration of the initial twisted Higgs bundle.
The Corlette-Donaldson-Hitchin-Simpson's correspondence states that, on a compact Kähler manifold $(X, ω)$, there is a one-to-one correspondence between the moduli space of semisimple flat complex vector bundles and the moduli space of poly-stable Higgs bundles with vanishing Chern numbers. In this paper, we extend this correspondence to the projectively flat bundles case. We prove that there is an equivalence of categories between the category of $ω$-semi-stable (poly-stable) Higgs bundles $(E, \overline{\partial}_{E}, ϕ)$ with $(2rc_{2}(E)-(r-1)c_{1}^{2}(E))\cdot [ω]^{n-2}=0 $ and the category of (semi-simple) projectively flat bundles $(E, D)$ with $\sqrt{-1}F_{D}=α\otimes \mbox{Id}_{E}$ for some real (1,1)-form $α$. Furthermore, we also establish the above correspondence on some compact non-Kähler manifolds. As its application, we obtain a vanishing theorem of characteristic classes of projectively flat bundles.