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Parabolic dimensional reductions of 11-dimensional supergravity
Analysis & PDE ( IF 1.8 ) Pub Date : 2021-08-22 , DOI: 10.2140/apde.2021.14.1333
Teng Fei , Bin Guo , Duong H. Phong

Ansatze are constructed under which the solutions of 11-dimensional supergravity must be stationary points of a parabolic flow on a Riemannian manifold M10p . This parabolic flow turns out to be the Ricci flow coupled to a scalar field, a (3p)-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.



中文翻译:

11维超重力的抛物线降维

Ansatze 被构建,在该条件下,11 维超重力的解必须是黎曼流形上抛物线流的驻点 10- . 这个抛物线流被证明是耦合到一个标量场的 Ricci 流,一个(3-)- 形式,和 4-形式。这允许引入从抛物线偏微分方程到 11 维超引力解的搜索技术。作为第一步,建立流动长期存在的 Shi 型估计和标准。

更新日期:2021-08-23
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