【摘 要】
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We prove Li-Yau type gradient bound for the heat equation either on fixed manifolds or on Ricci flows.In the former case the curvature condition is |Ric-|∈
【出 处】
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International Workshop on Conformal Geometry and Geometric P
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We prove Li-Yau type gradient bound for the heat equation either on fixed manifolds or on Ricci flows.In the former case the curvature condition is |Ric-|∈ Lp for some p > n/2,or supM∫M |Ric-|2(y)d2-n(x,y)dy <∞,where n is the dimension of the manifold.In the later case,then one only needs scalar curvature being bounded.We will explain why the conditions are nearly optimal and give an application on extending Colding-Nabers result.The Li-Yau bound on the heat equation seems to be the first one allowing Ricci curvatures not bounded from below.This is joint work with Richard H.Bamler and Meng Zhu.
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