| Full text | |
| Author(s): |
Dwivedi, Shubham
;
Loubeau, Eric
;
Earp, Henrique Sa
Total Authors: 3
|
| Document type: | Journal article |
| Source: | ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE; v. 25, n. 1, p. 65-pg., 2024-01-01. |
| Abstract | |
We formulate and study the isometric flow of 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 D Spin(7) subset of SO(8), obtaining conditions for long-time existence, via a monotonicity formula along the flow, which leads to an "-regularity theorem. Moreover, we prove Cheeger-Gromov and Hamilton -type compactness theorems for the solutions of the harmonic flow, and we characterise Type -I singularities as being modelled on shrinking solitons. We also establish a Bryant -type description of isometric Spin(7)-structures, based on squares of spinors, which may be of independent interest. (AU) | |
| FAPESP's process: | 18/21391-1 - Gauge theory and algebraic geometry |
| Grantee: | Marcos Benevenuto Jardim |
| Support Opportunities: | Research Projects - Thematic Grants |