Abstract
Let [Formula: see text] be an [Formula: see text]-dimensional compact self-shrinker in [Formula: see text] with smooth boundary [Formula: see text]. In this paper, we study eigenvalues of the operator [Formula: see text] on [Formula: see text], where [Formula: see text] is defined by [Formula: see text] with [Formula: see text] denoting a positive definite (0,2)-tensor field on [Formula: see text]. We obtain “universal” inequalities for eigenvalues of the operator [Formula: see text]. These inequalities generalize the result of Cheng and Peng in [Estimates for eigenvalues of [Formula: see text] operator on self-shrinkers, Commun. Contemp. Math. 15(6) (2013), Article ID:1350011, 23 pp.]. Furthermore, we also consider the case that equalities occur.
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