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See detailLong time existence and bounded scalar curvature in the Ricci-harmonic flow
Li, Yi UL

in Journal of Differential Equations (2018), 265(1), 69-97

In this paper we study the long time existence of the Ricci-harmonic flow in terms of scalar curvature and Weyl tensor which extends Cao's result \cite{Cao2011} in the Ricci flow. In dimension four, we ... [more ▼]

In this paper we study the long time existence of the Ricci-harmonic flow in terms of scalar curvature and Weyl tensor which extends Cao's result \cite{Cao2011} in the Ricci flow. In dimension four, we also study the integral bound of the ``Riemann curvature'' for the Ricci-harmonic flow generalizing a recently result of Simon \cite{Simon2015}. [less ▲]

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See detailHarnack estimates for a heat-type equation under the Ricci flow
Li, Yi UL; Zhu, Xiaorui

in Journal of Differential Equations (2016), 260(4), 3270-3301

In this paper, we consider the gradient estimates for a positive solution of the nonlinear parabolic equation ∂tu=Δtu+hup∂tu=Δtu+hup on a Riemannian manifold whose metrics evolve under the Ricci flow. Two ... [more ▼]

In this paper, we consider the gradient estimates for a positive solution of the nonlinear parabolic equation ∂tu=Δtu+hup∂tu=Δtu+hup on a Riemannian manifold whose metrics evolve under the Ricci flow. Two Harnack inequalities and other interesting results are obtained. [less ▲]

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