Eigenvalues of the Laplacian acting on $p$-forms and metric conformal deformations
نویسندگان
چکیده
منابع مشابه
Eigenvalues of the Laplacian acting on p - forms and metric conformal deformations
Let (M,g) be a compact connected orientable Riemannian manifold of dimension n ≥ 4 and let λk,p(g) be the k-th positive eigenvalue of the Laplacian ∆g,p = dd +dd acting on differential forms of degree p on M . We prove that the metric g can be conformally deformed to a metric g, having the same volume as g, with arbitrarily large λ1,p(g ) for all p ∈ [2, n − 2]. Note that for the other values o...
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Abstract. In this paper, we investigate critical points of the Laplacian’s eigenvalues considered as functionals on the space of Riemmannian metrics or a conformal class of metrics on a compact manifold. We obtain necessary and sufficient conditions for a metric to be a critical point of such a functional. We derive specific consequences concerning possible locally maximizing metrics. We also c...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2005
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-05-08005-6