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Li-Yau Harnack Estimates for a Heat-Type Equation Under the Geometric Flow
Potential Analysis ( IF 1.0 ) Pub Date : 2018-10-25 , DOI: 10.1007/s11118-018-9739-x Yi Li , Xiaorui Zhu
Potential Analysis ( IF 1.0 ) Pub Date : 2018-10-25 , DOI: 10.1007/s11118-018-9739-x Yi Li , Xiaorui Zhu
In this paper, we consider the gradient estimates for a postive solution of the nonlinear parabolic equation ∂tu = Δtu + hup on a Riemannian manifold whose metrics evolve under the geometric flow ∂tg(t) = − 2Sg(t). To obtain these estimate, we introduce a quantity \(\underline {\boldsymbol {S}}\) along the flow which measures whether the tensor Sij satisfies the second contracted Bianchi identity. Under conditions on Ricg(t),Sg(t), and \(\underline {\boldsymbol {S}}\), we obtain the gradient estimates.
中文翻译:
几何流下热型方程的Li-Yau Harnack估计
在本文中,我们考虑了非线性抛物线方程的正解的梯度估计∂吨Ù =Δ吨Ü + ħ Ü p上的黎曼流形,其度量的几何流动下演变∂吨克(吨)= - 2小号克(t)。为了获得这些估计,我们在流中引入了一个量\(\下划线{\ boldsymbol {S}} \),该量测量张量S i j是否满足第二个压缩的Bianchi身份。在Ric g(t),S g(t)和\(\下划线{\ boldsymbol {S}} \),我们获得梯度估计。
更新日期:2018-10-25
中文翻译:
几何流下热型方程的Li-Yau Harnack估计
在本文中,我们考虑了非线性抛物线方程的正解的梯度估计∂吨Ù =Δ吨Ü + ħ Ü p上的黎曼流形,其度量的几何流动下演变∂吨克(吨)= - 2小号克(t)。为了获得这些估计,我们在流中引入了一个量\(\下划线{\ boldsymbol {S}} \),该量测量张量S i j是否满足第二个压缩的Bianchi身份。在Ric g(t),S g(t)和\(\下划线{\ boldsymbol {S}} \),我们获得梯度估计。