Energy functionals and soliton equations for G_2-forms

Abstract

We extend short-time existence and stability of the Dirichlet energy flow as proven in a previous paper by the authors to a broader class of energy functionals. Furthermore, we derive some monotonely decreasing quantities for the Dirichlet energy flow and investigate an equation of soliton type. In particular, we show that nearly parallel G_2-structures satisfy this soliton equation and study their infinitesimal soliton deformations.

22 pages, typos corrected, reference added

Cited by in corpus (4)

• Short-time behaviour of a modified Laplacian coflow of G2-structures
• The spinorial energy functional on surfaces
• A spinorial energy functional: critical points and gradient flow
• Laplacian Solitons and Symmetry in G_2-geometry