Abstract
In this paper, we study the compactness of a boundary value problem for hyperkähler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkähler 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.
Citation
Hongyi Liu. "A compactness theorem for hyperkähler 4-manifolds with boundary." Duke Math. J. 173 (6) 1177 - 1225, 15 April 2024. https://doi.org/10.1215/00127094-2023-0037
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