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Long-time existence of some geometric flows with bounded scalar curvature
Chuanhuan Li, Yi Li
The analysis of singularities in scalar curvature is a classical problem. In this survey, we investigate the behavior of scalar curvature under several geometric flows, with a focu…
Real analyticity of the modified Laplacian coflow
Chuanhuan Li, Yi Li
Let (M,Ï(t))_{t\in[0, T]} be a solution of the modified Laplacian coflow (1.3) with coclosed G_{2}-structures on a compact 7-dimensional M. We improve Chen's Shi-type estimate [5]…
Curvature pinching estimate under the Laplacian G_{2} flow
Chuanhuan Li, Yi Li
In this paper, we derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and the C^{1} norm of the Weyl tensor under the Laplacian G_{2} flow for c…
Parabolic frequency monotonicity for two nonlinear equations under Ricci flow
Chuanhuan Li, Yi Li, Kairui Xu +1
In this paper, we consider the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds. We obtain the monotonicity…
Gradient estimates and parabolic frequency under the Laplacian G_2 flow
Chuanhuan Li, Yi Li, Kairui Xu
In this paper, we consider the Laplacian G_2 flow on a closed seven-dimensional manifold M with a closed G_2-structure. We first obtain the gradient estimates of positive solutions…