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arXiv · 1708.01649

Boundary value problems in dimensions seven, four and three related to exceptional holonomy

Simon Donaldson
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Abstract

In the paper we introduce a boundary value problem for a G_{2} structure on a 7-manifold with boundary, with prescribed 3-form on the boundary. We make some general observations about this problem and then study in more detail reductions to 4 and 3 dimensions by imposing symmetry. The 3-dimensional reduction admits a dual variational formulation in terms of solutions of the real Monge-Ampere equation

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Simon Donaldson. 2017-08-04. Boundary value problems in dimensions seven, four and three related to exceptional holonomy. https://arxiv.org/abs/1708.01649

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