Abstract
In this paper, we give a sharp lower bound for the first (nonzero) p-eigenvalue on a compact Finsler manifold M without boundary or with convex boundary if the weighted Ricci curvature RicciN is bounded from below by a constant K in terms of the diameter d of a manifold, dimension, K, p and N. In particular, if RicciN is non-negative, then the first p-eigenvalue is bounded from below by $$(p - 1){({\textstyle{{{\pi _p}} \over d}})^p}$$, and the equality holds if and only if M is either a circle or a segment.
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