Abstract
In the paper we consider a closed Riemannian manifold M with a time-dependent Riemannian metric g ij (t) evolving by ∂ t g ij = −2S ij , where S ij is a symmetric two-tensor on (M,g(t)). We prove some differential Harnack inequalities for positive solutions of heat equations with potentials on (M,g(t)). Some applications of these inequalities will be obtained.
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The work is supported by the Foundation of Yangzhou University 2011CXJ004 and NSFC 11101352.
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Fang, S. Differential Harnack inequalities for heat equations with potentials under geometric flows. Arch. Math. 100, 179–189 (2013). https://doi.org/10.1007/s00013-013-0482-7
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DOI: https://doi.org/10.1007/s00013-013-0482-7