The lower bounds for the first eigenvalue of the biharmonic and $p$-biharmonic operators on Finsler manifolds

Abstract

In this paper, we are going to estimate the lower bounds for the first eigenvalues of the buckling problem and clamped plate problem by considering a positive lower bound for the weighted Ricci curvature. Also, we extended the results for the $p$-biharmonic operator and we prove a Lichnerowicz-Obata-Cheng type estimate for the biharmonic operators.