A compactness theorem for hyperkaehler 4-manifolds with boundary
Differential Geometry
2022-02-16 v1
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.
Cite
@article{arxiv.2202.07151,
title = {A compactness theorem for hyperkaehler 4-manifolds with boundary},
author = {Hongyi Liu},
journal= {arXiv preprint arXiv:2202.07151},
year = {2022}
}