An elliptic boundary value problem for $G_{2}$ structures

Simon Donaldson

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arXiv · 1801.01806

An elliptic boundary value problem for $G_{2}$ structures

Simon Donaldson

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Abstract

We show that the $G_{2}$ holonomy equation on a manifold with boundary, with prescribed 3-form on the boundary, is elliptic. The main point is to set up a suitable linear elliptic boundary value problem. This result leads to a deformation theory. In particular we establish the existence of certain $G_{2}$ cobordisms between two small deformations of a Calabi-Yau 3-fold.

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Simon Donaldson. 2018-01-05. An elliptic boundary value problem for $G_{2}$ structures. https://arxiv.org/abs/1801.01806

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