Vol. 14, No. 5, 2021

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Parabolic dimensional reductions of 11-dimensional supergravity

Teng Fei, Bin Guo and Duong H. Phong

Vol. 14 (2021), No. 5, 1333–1361
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 $\left(3-p\right)$-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.

Keywords
11-dimensional supergravity, Shi-type estimates
Primary: 53Z05