Existence, Convergence and Limit Map of the Laplacian Flow

Feng Xu; Rugang Ye

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arXiv · 0912.0074

Existence, Convergence and Limit Map of the Laplacian Flow

Feng Xu·Rugang Ye

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Abstract

We prove short time existence and uniqueness of the Laplacian flow starting at an arbitrary closed $G_2$-structure. We establish long time existence and convergence of the Laplacian flow starting near a torsion-free $G_2$-structure. We analyze the limit map of the Laplacian flow in relation to the moduli space of torsion-free $G_2$-structures. We also present a number of results which constitute a fairly complete algebraic and analytic basis for studying the Laplacian flow.

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BibTeX RIS

Feng Xu, Rugang Ye. 2009-12-01. Existence, Convergence and Limit Map of the Laplacian Flow. https://arxiv.org/abs/0912.0074

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