# The sharp lower bound of the first Dirichlet eigenvalue for geodesic balls

@article{Wang2021TheSL, title={The sharp lower bound of the first Dirichlet eigenvalue for geodesic balls}, author={Haibin Wang and Guoyi Xu and Jie Zhou}, journal={Mathematische Zeitschrift}, year={2021}, volume={300}, pages={2063-2068} }

On complete noncompact Riemannian manifolds with non-negative Ricci curvature, Li–Schoen proved the uniform Poincaré inequality for any geodesic ball. In this note, we obtain the sharp lower bound of the first Dirichlet eigenvalue of such geodesic balls, which implies the sharp Poincaré inequality for geodesic balls.

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