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arXiv · 1304.5268

Eigenvalue estimates for a class of elliptic differential operators on compact manifolds

Hilário Alencar·Gregório Silva Neto·Detang Zhou
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Abstract

The motivation of this paper is to study a second order elliptic operator which appears naturally in Riemannian geometry, for instance in the study of hypersurfaces with constant $r$-mean curvature. We prove a generalized Bochner-type formula for such a kind of operators and as applications we obtain some sharp estimates for the first nonzero eigenvalues in two special cases. These results can be considered as generalizations of the Lichnerowicz-Obata Theorem.

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Hilário Alencar, Gregório Silva Neto, Detang Zhou. 2013-04-18. Eigenvalue estimates for a class of elliptic differential operators on compact manifolds. https://doi.org/10.1007/s00574-015-0102-1

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