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arXiv · 2202.07151

A compactness theorem for hyperkaehler 4-manifolds with boundary

Hongyi Liu
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Abstract

In this paper, we study the compactness of a boundary value problem for hyperkaehler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkaehler triples converges smoothly up to diffeomorphisms if and only if their restrictions to the boundary converge smoothly up to diffeomorphisms. We also generalize this result to torsion-free hypersymplectic triples.

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Hongyi Liu. 2022-02-15. A compactness theorem for hyperkaehler 4-manifolds with boundary. https://arxiv.org/abs/2202.07151

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