Abstract
Given a complete, smooth metric measure space \((M,g,e^{-f}dv)\) with the Bakry–Émery Ricci curvature bounded from below, various gradient estimates for solutions of the following general f-heat equations
and
are studied. As by-product, we obtain some Liouville-type theorems and Harnack-type inequalities for positive solutions of several nonlinear equations including the Schrödinger equation, the Yamabe equation, and Lichnerowicz-type equations as special cases.
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Dung, N.T., Khanh, N.N. & Ngô, Q.A. Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces. manuscripta math. 155, 471–501 (2018). https://doi.org/10.1007/s00229-017-0946-3
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DOI: https://doi.org/10.1007/s00229-017-0946-3