• Corpus ID: 237504167

Harmonic flow of $\mathrm{Spin}(7)$-structures

  title={Harmonic flow of \$\mathrm\{Spin\}(7)\$-structures},
  author={Shubham Dwivedi and Eric Loubeau and Henrique N. S{\'a} Earp},
We formulate and study the isometric flow of $\mathrm{Spin}(7)$-structures on compact $8$-manifolds, as an instance of the harmonic flow of geometric structures. Starting from a general perspective, we establish Shi-type estimates and a correspondence between harmonic solitons and self-similar solutions for arbitrary isometric flows of $H$-structures. We then specialise to $H=\mathrm{Spin}(7)\subset\mathrm{SO}(8)$, obtaining conditions for long-time existence, via a monotonicity formula along…