We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in with boundary ∂Ω, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau’s result.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-5,
author = {Haizhong Li and Linlin Su},
title = {The gaps in the spectrum of the Schr\"odinger operator},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {91-102},
zbl = {1081.35062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-5}
}
Haizhong Li; Linlin Su. The gaps in the spectrum of the Schrödinger operator. Banach Center Publications, Tome 68 (2005) pp. 91-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-5/