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arXiv · 1603.07702

Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical K\"ahler manifolds

Adam Jacob·Thomas Walpuski
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Abstract

We prove an analogue of the Donaldson-Uhlenbeck-Yau theorem for asymptotically cylindrical K\"ahler manifolds: If $\mathscr{E}$ is a reflexive sheaf over an ACyl K\"ahler 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 $L^2_{\mathrm{loc}}$ 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].

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Adam Jacob, Thomas Walpuski. 2016-03-24. Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical K\"ahler manifolds. https://doi.org/10.1080/03605302.2018.1517792

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