Volume 4, Issue 4
An Eigenvalue Problem on Negatively Curved Manifolds

J. Part. Diff. Eq.,4(1991),pp.1-8

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• Abstract

Consider the eigenvalue problem: Δgu - λKu = 0 \quad in D where D is the unit disc of the complex plane, g is a complete metric conformal to the Poincaré metric on D, and K is the Gaussian curvature. It is shown that if λ > \frac{1}{2} (λ > \frac{1}{4}in the case of K ≤ 0), then the above problem has no positive solutions.

• History

Published online: 1991-04

• Keywords