PARABOLIC DIMENSIONAL REDUCTIONS OF 11-DIMENSIONAL SUPERGRAVITY

Teng Fei, Bin Guo, Duong H. Phong

Research output: Contribution to journalArticlepeer-review

Abstract

Ansatze are constructed under which the solutions of 11-dimensional supergravity must be stationary points of a parabolic flow on a Riemannian manifold M 10- p. This parabolic flow turns out to be the Ricci flow coupled to a scalar field, a (3- p)-form, and a 4-form. This allows the introduction of techniques from parabolic partial differential equations to the search of solutions to 11-dimensional supergravity. As a first step, Shi-type estimates and criteria for the long-time existence of the flow are established.

Original languageEnglish (US)
Pages (from-to)1333-1361
Number of pages29
JournalAnalysis and PDE
Volume14
Issue number5
DOIs
StatePublished - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

Keywords

  • 11-dimensional supergravity
  • Shi-type estimates

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