Bär, Christian Extrinsic bounds for eigenvalues of the Dirac operator. (English) Zbl 0921.58065 Ann. Global Anal. Geom. 16, No. 6, 573-596 (1998). The author derives upper eigenvalue estimates for the Dirac operator of a closed hypersurface of Euclidean space resp. a space carrying Killing spinors. In the estimates the integral over the squared mean curvature occurs and the relation with the Willmore inequality is discussed. Reviewer: H.-B.Rademacher (Leipzig) Cited in 4 ReviewsCited in 75 Documents MSC: 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:eigenvalue; Dirac operator; Killing spinor; Willmore inequality; mean curvature PDFBibTeX XMLCite \textit{C. Bär}, Ann. Global Anal. Geom. 16, No. 6, 573--596 (1998; Zbl 0921.58065) Full Text: DOI arXiv