LOCAL HARNACK ESTIMATE FOR YAMABE FLOW ON LOCALLY CONFORMALLY FLAT MANIFOLDS

摘要

In this paper, we first prove the local derivatives 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 <= Mg-ab, where 0 <= m(t) <= M and m'(t) >= (4n+1)m(t)M, on t is an element of [0, r(2)]. As a corollary, we get a sharp derivative estimate of scalar curvature in some directions.