A compactness theorem for hyperkahler 4-manifolds with boundary
A compactness theorem for hyperkahler 4-manifolds with boundary
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Hongyi Liu, University of California, Berkeley
A hyperk盲hler triple on a compact 4-manifold with boundary is a triple of symplectic 2-forms that are pointwise orthonormal with respect to the wedge product. It defines a Riemannian metric of holonomy contained in SU(2) and its restriction to the boundary defines a framing. In this talk, I will show that听a sequence of hyperk盲hler triples converges smoothly up to diffeomorphims if their restrictions to the boundary converge smoothly up to diffeomorphisms, under certain topological assumptions and the 鈥減ositive mean curvature鈥 condition of the boundary framings.