A heat flow for special metrics

Abstract

On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in $G_2$. We prove short-time existence and uniqueness for its negative gradient flow. Furthermore, we show that the flow exists for all times and converges modulo diffeomorphisms to some critical point for any initial condition sufficiently $C^{\infty }$-close to a critical point.

35 pages, slightly revised

References in corpus (1)

• Existence, Convergence and Limit Map of the Laplacian Flow

Cited by in corpus (5)

• Soliton solutions for the Laplacian coflow of some $G_2$-structures with symmetry
• The spinorial energy functional on surfaces
• A spinorial energy functional: critical points and gradient flow
• Laplacian Solitons and Symmetry in G_2-geometry
• Energy functionals and soliton equations for G_2-forms