Evolution of the first eigenvalue along the inverse mean curvature flow in space forms (Q6140911)

The authors establish monotonicity properties of the first nonzero eigenvalue of the Laplacian and the \(p\)-Laplacian in hyperbolic space and in the sphere. They prove that the first nonzero eigenvalues of the Laplacian and \(p\)-Laplacian are monotonically decreasing along the inverse mean curvature flow the hyperbolic space and in the sphere. The authors apply these results to obtain a lower bound for the first nonzero eigenvalue.