Eigenvalues of a (p, q)-Laplacian System Under the Mean Curvature Flow

摘要

In this paper, we derive the evolution equation for the first eigenvalue of a class of (p, q)-Laplacian system. Moreover, by imposing some conditions on the mean curvature of the initial hypersurface, we can show that the first eigenvalue of a class of (p, q)-Laplacian system is monotonic under the volume-preserving mean curvature flow and unnormalized mean curvature flow.