June 7, 2022
TITLE: A compactness theorem for hyperkahler 4 manifolds with boundary

ABSTRACT:
A hyperkahler triple on a 4-manifold with boundary is a triple of symplectic
2-forms that are pointwise orthonormal with respect to the wedge product, so
its restriction to the boundary 3-manifold is a closed framing. Motivated by
previous work of Bryant, Fine-Lotay-Singer on the hyperkahler triple filling
problem, and a dimension 4 reduction of Donaldson’s elliptic boundary value
problem for G2 structures, we discuss some recent progress towards the
compactness part of these problems on compact 4-manifolds with boundary.