Curvature estimates on a parabolic flow of Fei-Guo-Phong

TL;DR

This paper introduces a new criterion for the long-time existence of a parabolic flow related to 11-dimensional supergravity, relying on Ricci curvature, the 4-form, and its gradient, simplifying previous conditions.

Contribution

The authors derive a novel criterion for the flow's long-time existence that depends only on Ricci curvature, the 4-form, and its gradient, improving upon previous curvature-based conditions.

Findings

New criterion involves Ricci curvature and form gradient

Simplifies previous long-time existence conditions

Applicable to flows in supergravity contexts

Abstract

In \cite{FGP}, Fei, Guo and Phong established a criteria for the long-time existence of their parabolic flow from $11$-dimensional supergravity, which involves Riemannian curvatures ${\rm Rm}(g(t))$ and 4-forms $F(t)$. In this paper, we obtain a new criteria for the long-time existence of the same flow, which involves only Ricci curvatures ${\rm Ric}(g(t))$, $F(t)$, but as well as $\nabla_{g(t)}F(t)$.