On the first Hodge eigenvalue of isometric immersions
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- by Alessandro Savo PDF
- Proc. Amer. Math. Soc. 133 (2005), 587-594 Request permission
Abstract:
We give an extrinsic upper bound for the first positive eigenvalue of the Hodge Laplacian acting on $p$-forms on a compact manifold without boundary isometrically immersed in $\mathbf R^n$ or $\mathbf S^n$. The upper bound generalizes an estimate of Reilly for functions; it depends on the mean value of the squared norm of the mean curvature vector of the immersion and on the mean value of the scalar curvature. In particular, for minimal immersions into a sphere the upper bound depends only on the degree, the dimension and the mean value of the scalar curvature.References
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Additional Information
- Alessandro Savo
- Affiliation: Dipartimento di Metodi e Modelli Matematici, Università di Roma, La Sapienza, Via Antonio Scarpa 16, 00161 Roma, Italy
- Email: savo@dmmm.uniroma1.it
- Received by editor(s): January 22, 2003
- Published electronically: August 25, 2004
- Communicated by: Jozef Dodziuk
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 587-594
- MSC (2000): Primary 58J50; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-04-07702-0
- MathSciNet review: 2093083