Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kähler manifolds

Abstract

We prove an analogue of the Donaldson-Uhlenbeck-Yau theorem for asymptotically cylindrical Kähler manifolds: If $\mathcal{E}$ is a reflexive sheaf over an ACyl Kähler manifold, which is asymptotic to a $\mu$-stable holomorphic vector bundle, then it admits an asymptotically translation-invariant protectively Hermitian Yang-Mills metrics (with curvature in $L_{\mathrm{loc}}^2$ across the singular set). Our proof combines the analytic continuity method of Uhlenbeck and Yau [UY86] with the geometric regularization scheme introduced by Bando and Siu [BS94].

v3 corrects an error in the proof of the uniform bound on the Neumann-Poincaré constant in Proposition 6.1

References in corpus (1)

• $G_2$-instantons over twisted connected sums: an example

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