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Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior

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Date
2011-01-11
Authors
Bryant, R
Xu, F
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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 article
Subject
math.DG
math.DG
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https://hdl.handle.net/10161/13140
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Scholars@Duke

Bryant

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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