A COMPACTNESS THEOREM FOR HYPERKÄHLER 4-MANIFOLDS WITH BOUNDARY

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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.

Original languageEnglish (US)
Pages (from-to)1177-1225
Number of pages49
JournalDuke Mathematical Journal
Volume173
Issue number6
DOIs
StatePublished - Apr 15 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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