Estimates for eigenvalues of the operator $L_r$

preprint2015arXivOpen access

In this paper, we consider an eigenvalue problem of the elliptic operator $L_r={\rm div}(T^r\nabla\cdot )$ on compact submanifolds in arbitrary codimension of space forms $\mathbb{R}^N(c)$ with $c\geq0$ . Our estimates on eigenvalues are sharp.

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Estimates for eigenvalues of the operator $L_r$

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Estimates for eigenvalues of the operator LrL_rLr​

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Estimates for eigenvalues of the operator $L_r$