Conformal upper bounds for the first eigenvalue of the p-Laplacian
Let M be a compact, connected, m-dimensional manifold without boundary and p>1. For 1 m, we show that any conformal class of Riemannian metrics on M contains metrics of volume one with λ_{1,p} arbitrarily large. As a consequence, we obtain that in two dimensions λ_{1,p} is uniformly bounded on the space of Riemannian metrics of volume one if 1 2.
math.DG↗