A compactness theorem for hyperkaehler 4-manifolds with boundary
- Resource Type
- Working Paper
- Authors
- Liu, Hongyi
- Source
- Subject
- Mathematics - Differential Geometry
- Language
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.