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Local Harnack Estimate for Yamabe Flow on Locally Conformally Flat Manifolds

2008
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Asian Journal of Mathematics
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In this paper, we first prove the local derivative estimate of curvature under Yamabe flow, and then by using it obtain the local Harnack estimate of Yamabe flow on locally conformally flat manifolds, under the condition −m(t)g ab ≤ R ab ≤ M g ab , where 0 ≤ m(t) ≤ M and m ′ (t) ≥ (4n + 1)m(t)M , on t ∈ [0, r 2 ]. As a corollary, we get a sharp derivative estimate of scalar curvature in some directions. 1. Introduction. The Harnack estimate of geometry flow is also called Li-Yau-Hamilton

doi:10.4310/ajm.2008.v12.n4.a8
fatcat:ygzmp7v2hbdkrm5mg6wai2efrm