Existence, Convergence and Limit Map of the Laplacian Flow

2009/12/01 by Feng Xu, Xu, Feng, Rugang Ye +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0912.0074

Abstract

We prove short time existence and uniqueness of the Laplacian flow starting at an arbitrary closed G₂-structure. We establish long time existence and convergence of the Laplacian flow starting near a torsion-free G₂-structure. We analyze the limit map of the Laplacian flow in relation to the moduli space of torsion-free G₂-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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