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题目：Gradient Estimates and Liouville Theorems for Lichnerowicz Equations

报告人：黄平亮 教授 （上海大学）

地点：致远楼101室

时间：2021年10月21日 10:30-11:30

摘要：We study the positive solutions to a class of general semilinear elliptic equations ∆u(x) + uh(ln u) = 0 defined on a complete Riemannian manifold (M, g) with Ric(g) ≥ −Kg, and obtain the Li-Yau type gradient estimates of positive solutions to these equations which do not depend on the bounds of the solutions and the Laplacian of the distance function on (M, g). We also obtain some Liouville-type theorems for these equations when (M, g) is noncompact and Ric(g) ≥ 0 and establish some Harnack inequalities as consequences. Then, as applications of main theorem we extend our techniques to the Lichnerowicz-type equations

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