A generalized Omori-Yau maximum principle and Liouville-type theorems for a second-order linear semi-elliptic operator

Details A generalized Omori-Yau maximum principle and Liouville-type theorems for a second-order linear semi-elliptic operator A generalized Omori-Yau maximum principle and Liouville-type theorems for a second-order linear semi-elliptic operator

2011-11-15

arxiv.org/abs/1111.3456v1

Mathematics

Differential Geometry

Scientific paper

We generalize the Omori-Yau almost maximum principle of the Laplace-Beltrami operator on a complete Riemannian manifold $M$ to a second-order linear semi-elliptic operator $\widetilde{\Delta}$ with bounded coefficients and no zeroth order term. Using this result, we prove some Liouville-type theorems for a real-valued $C^{2}$ function $f$ on $M$ satisfying $\widetilde{\Delta} f \geq F(f)+ H(|\nabla f|) $ for real-valued continuous functions $F$ and $H$ on $\Bbb R$ such that $H(0)=0$.

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