Abstract
We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature, if its first closed (resp. Neumann) eigenvalue of Finsler-Laplacian attains the sharp lower bound, then M is isometric to a circle (resp. a segment). Moreover, a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated. These generalize the corresponding results in recent literature.
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Yin, S., He, Q. & Shen, Y. On the first eigenvalue of Finsler manifolds with nonnegative weighted Ricci curvature. Sci. China Math. 57, 1057–1070 (2014). https://doi.org/10.1007/s11425-013-4707-9
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DOI: https://doi.org/10.1007/s11425-013-4707-9