Abstract
In this paper, we establish a logarithmic Sobolev inequality in complete Finsler measure spaces. As its applications, we prove the existence of solutions of eigenvalue problem for the Finsler Laplacian. Finally, we obtain a Lichnerowicz type theorem which shows that for a complete Finsler measure space with Ric∞≥K>0, the first eigenvalue has lower bound K2.
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