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Diffusion-type operators, Liouville theorems and gradient estimates on complete manifolds

✍ Scribed by Paolo Mastrolia; Marco Rigoli


Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
952 KB
Volume
72
Category
Article
ISSN
0362-546X

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Gradient Estimates and a Liouville Type
✍ E.R. Negrin πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 164 KB

In this paper, we derive a Liouville type theorem on a complete Riemannian manifold without boundary and with nonnegative Ricci curvature for the equation \(\Delta u(x)+h(x) u(x)=0\), where the conditions \(\lim _{r \rightarrow x} r^{-1} \cdot \sup _{x \in B_{p}(r)}|\nabla h(x)|=0\) and \(h \geqslan