Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior

By Robert L. Bryant, Fengjun Xu. 2011

86 citations recorded by the source corpus.

We prove short time existence and uniqueness of solutions to the Laplacian flow for closed $G_2$ structures on a compact manifold $M^7$. The result was claimed in \cite{BryantG2}, but its proof has never appeared.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/07ce20a33d6b927c75d3aa364d3046e65c83d8a2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. V. Manero
2. Anna Fino
3. M. Fernández
4. L. Ugarte
5. Luigi Vezzoni
6. Adriano Tomassini

In Geometry and Topology

1. Anna Fino
2. V. Manero
3. M. Fernández
4. Adriano Tomassini
5. L. Ugarte
6. Luigi Vezzoni

Citations in the corpus

• Laplacian Flow of Closed G$$_2$$2-Structures Inducing Nilsolitons (2013, background): “1 [4] If M is compact, then (18) has a unique solution for a short time 0 ≤ t < , with depending on φ = φ(0).”