Abstract
We prove that, for a Finsler space, if the weighted Ricci curvature is bounded below by a positive number and the diam attains its maximal value, then it is isometric to a standard Finsler sphere. As an application, we show that the first eigenvalue of the Finsler-Laplacian attains its lower bound if and only if the Finsler manifold is isometric to a standard Finsler sphere, and moreover, we obtain an explicit 1-st eigenfunction on the sphere.
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