Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior
Abstract
We prove short time existence and uniqueness of solutions to the Laplacian flow for
closed $G_2$ structures on a compact manifold $M^7$. The result was claimed in \cite{BryantG2},
but its proof has never appeared.
Type
Journal articlePermalink
https://hdl.handle.net/10161/13140Collections
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Show full item recordScholars@Duke
Robert Bryant
Phillip Griffiths Professor of Mathematics
My research concerns problems in the geometric theory of partial differential equations.
More specifically, I work on conservation laws for PDE, Finsler geometry, projective
geometry, and Riemannian geometry, including calibrations and the theory of holonomy.
Much of my work involves or develops techniques for studying systems of partial differential
equations that arise in geometric problems. Because of their built-in invariance
properties, these systems often have specia
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