An elliptic boundary value problem for $G_{2}$ structures
Differential Geometry
2019-01-23 v2
Abstract
We show that the 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 cobordisms between two small deformations of a Calabi-Yau 3-fold.
Cite
@article{arxiv.1801.01806,
title = {An elliptic boundary value problem for $G_{2}$ structures},
author = {Simon Donaldson},
journal= {arXiv preprint arXiv:1801.01806},
year = {2019}
}
Comments
Some minor changes. This is the final version, to appear in Annales de l'Institut Fourier