On the discreteness of the spectrum of the Laplacian on noncompact Riemannian manifolds
2011 (English)In: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 87, no 3, 469-491 p.Article in journal (Refereed) Published
Necessary and sufficient conditions for the discreteness of the Laplacian on a noncompact Riemannian manifold M are established in terms of the isocapacitary function of M. The relevant capacity takes a different form according to whether M has finite or infinite volume. Conditions involving the more standard isoperimetric function of M can also be derived, but they are only sufficient in general, as we demonstrate by concrete examples.
Place, publisher, year, edition, pages
International Press , 2011. Vol. 87, no 3, 469-491 p.
IdentifiersURN: urn:nbn:se:liu:diva-71562ISI: 000295439600002OAI: oai:DiVA.org:liu-71562DiVA: diva2:450513
Funding Agencies|MUIR||GNAMPA (INdAM)||UK Engineering and Physical Sciences Research Council|