Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 1, pp. 15-27 (2006)

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Eigenvalues of a natural operator of centro-affine and graph hypersurfaces

Bang-Yen Chen

Department of Mathematics, Michigan State University, East Lansing, Michigan 48824--1027, USA; e-mail: bychen@math.msu.edu

Abstract: In this article we obtain optimal estimates for the eigenvalues of a natural operator $K_{T^\#}$ for locally strongly convex centro-affine and graph hypersurfaces. Several immediate applications of our eigenvalue estimates are presented. We also provide examples to illustrate that our eigenvalue estimates are optimal.

Keywords: Centroaffine hypersurface, graph hypersurface, the operator, eigenvalue estimate.

Classification (MSC2000): 53A15, 53B20, 53B25; 53C40

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Electronic version published on: 9 May 2006. This page was last modified: 4 Nov 2009.

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