The Anomaly flow is a flow which implements the Green-Schwarz anomaly cancellation
mechanism originating from superstring theory, while preserving the conformally balanced …

This article is a broad-brush survey of two areas in differential geometry. While these two
areas are not usually put side-by-side in this way, there are several reasons for discussing …

We use the bracket flow/algebraic soliton approach to study the Laplacian flow of G 2‐
structures and its solitons in the homogeneous case. We prove that any homogeneous …

We continue the investigation of general geometric flows of $ G_2 $-structures initiated by
the third author in" Flows of $ G_2 $-structures, I." Specifically, we determine the possible …

A geometric flow on $6 $-dimensional symplectic manifolds is introduced which is motivated
by supersymmetric compactifications of the Type IIA string. The underlying structure turns out …

We prove that torsion-free $\mathrm {G} _2 $ structures are (weakly) dynamically stable
along the Laplacian flow for closed $\mathrm {G} _2 $ structures. More precisely, given a …

We develop a general approach to study geometric flows on homogeneous spaces. Our
main tool will be a dynamical system defined on the variety of Lie algebras called the …

While the Anomaly flow was originally motivated by string theory, its zero slope case is
potentially of considerable interest in non-Kähler geometry, as it is a flow of conformally …

We give the first examples of closed Laplacian solitons which are shrinking, and in particular
produce closed Laplacian flow solutions with a finite-time singularity. Extremally Ricci …

We study a flow of G _2 G 2-structures that all induce the same Riemannian metric. This
isometric flow is the negative gradient flow of an energy functional. We prove Shi-type …