Evolution of the First Eigenvalue of the (p; q)-Laplacian System Under Rescaled Yamabe Flow

Consider the triple (M, 9, du) as a smooth metric measure space and M is an n-dimensional compact Riemannian manifold without boundary, also dure 1dV is a weighted measure. We are going to investigate the evolution problem for the first eigenvalue of the weighted (p, q)-Laplacian system along the rescaled Yamabe flow and we hope find some monotonic quantities.