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On Harnack estimates for positive solutions of the heat equation on a complete manifold
Institution:1. Department of Electrical Engineering, Federal University of Juiz de Fora, Juiz de Fora, Brazil;2. Media Integrated Communication Laboratory, Graduate School of Engineering, Osaka University, Suita, Osaka, Japan;3. School of Earth, Energy and Environmental Engineering, Kitami Institute of Technology, Hokkaido, Japan;4. Strategic Research Projects Center, University of the Ryukyus, Senbaru, Okinawa, Japan;1. School of Mathematical Sciences and LPMC, Nankai University, 300071 Tianjin, China;2. Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany;3. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;1. Institute of Science and Technology, Austria;2. Moscow Inst. of Physics and Technology, Moscow, Russia;3. Alfréd Rényi Inst. of Math., MTA-ELTE Lendület Combinatorial Geometry Research Group, Dept. of Geometry, Loránd Eötvös University, Budapest, Hungary;1. EPFL SB, Station 8, CH-1015 Lausanne, Switzerland;2. Institute for advanced study, 1 Einstein Dr, Princeton, NJ 08540, United States of America;3. CNRS and Institut de Mathématiques de Toulouse, Université de Toulouse, 118 route de Narbonne, 31068, Toulouse, France
Abstract:We establish several new Harnack estimates for the nonnegative solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded by a positive or negative constant. This extends to symmetric diffusions whose generator satisfies a “curvature-dimension” inequality.
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