Finsler流形上的最大直径定理
The maximum diam theorem on Finsler manifolds
摘要：
证明了对于Finsler空间，如果加权里奇曲率有正数下界且直径达到其最大值，则它等距于标准Finsler球面.作为应用，我们证明了Finsler-Laplacian的第一特征值达到它的下界当且仅当Finsler流形等距于标准Finsler球面，并且得到了球面上的显式第一特征函数.
英文摘要：
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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