An Omori-Yau maximum principle for semi-elliptic operators and Liouville-type theorems

Abstract

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 $L$ 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 $Lf\ge F(f)+H(|\nabla f|)$ for real-valued continuous functions $F$ and $H$ on $\mathbb{R}$ such that $H(0)=0$.

References in corpus (2)

• A Remark on the Omori-Yau Maximum Principle
• Comparison Theorems in Lorentzian Geometry and applications to spacelike hypersurfaces

Cited by in corpus (1)

• Maximum principle for semi-elliptic trace operators and geometric applications