Conformal bounds for the first eigenvalue of the $(p,q)$-Laplacian system

Abstract

Consider $\left(M,g\right)$ as an $m$-dimensional compact connected Riemannian manifold without boundary. In this paper, we investigate the first eigenvalue ${\lambda }_{1,p,q}$ of the $\left(p,q\right)$-Laplacian system on $M$. Also, in the case of $p,q>n$ we will show that for arbitrary large ${\lambda }_{1,p,q}$ there exists a Riemannian metric of volume one conformal to the standard metric of ${\mathbb{S}}^m$.