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.

中文翻译：

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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 ${米}^{10-磷}$. 这个抛物线流被证明是耦合到一个标量场的 Ricci 流，一个$\left(3-磷\right)$- 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。