Upper bounds for the eigenvalues of the Laplace–Beltrami operator on a
hypersurface bounding a domain in some ambient Riemannian manifold are
given in terms of the isoperimetric ratio of the domain. These
results are applied to the extrinsic geometry of isometric
Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of
Crelle’s Journal. In the 190 years of its existence,
Crelle’s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals.