Ryan Hynd University of Pennsylvania The principle eigenvalue of Laplace's operator arises as a special number in a variety of problems. The corresponding eigenfunctions are also known to minimize Rayleigh's quotient and to appear in the study of the large time behavior of solutions of the heat equation. In this talk, we present analogs of these facts for p-ground states, which minimize a p-Rayleigh quotient and are involved in the large time behavior of a particular nonlinear flow.