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Complex Analysis and Geometry Seminar

A compactness theorem for hyperkähler 4-manifolds with boundary

Hongyi Liu

Location:  Hill 705
Date & time: Friday, 26 April 2024 at 10:30AM - 11:30AM

A hyperkähler 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 a sequence of hyperkähler triples converges smoothly up to diffeomorphims if their restrictions to the boundary converge smoothly up to diffeomorphisms, under certain topological assumptions and the “positive mean curvature” condition of the boundary framings.