Sharp bounds for eigenvalues and multiplicities on surfaces of revolution

Martin Engman

Vol. 186 (1998), No. 1, 29–37

DOI: 10.2140/pjm.1998.186.29

Abstract

For surfaces of revolution diffeomorphic to S², it is proved that (S²,can) provides sharp upper bounds for the multiplicities of all of the distinct eigenvalues. We also find sharp upper bounds for all the distinct eigenvalues and show that an infinite sequence of these eigenvalues are bounded above by those of (S²,can). An example of such bounds for a metric with some negative curvature is presented.

Milestones

Received: 29 January 1996

Published: 1 November 1998