Eigenvalue of $(p,q)$-Laplace system along the powers of mean curvature flow

Abstract

In this paper we derive the evolution equation of the first nonzero eigenvalue of the $(p,q)$ Laplace system under the unnormalized $H^k$-flow. By imposing some conditions on the mean curvature we prove the monotonicity of the first nonzero eigenvalue under the unnormalized $H^k$-flow.