Displaying similar documents to “Compact Kaehler manifolds and the eigenvalues of the Laplacian”

A minorization of the first positive eigenvalue of the scalar laplacian on a compact Riemannian manifold

Jacek Komorowski

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CONTENTSIntroduction.......................................................................................................... 51. A parametrix of tho laplacian................................................................................ 72. An estimation of the differential of an eigenfunction of the laplacian......... 163. A normal chart on a neighbourhood of a geodesic........................................ 274. Minorization of the first positive eigenvalue of the laplacian............................

Two new estimates for eigenvalues of Dirac operators

Wenmin Gong, Guangcun Lu (2016)

Annales Polonici Mathematici

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We establish lower and upper eigenvalue estimates for Dirac operators in different settings, a new Kirchberg type estimate for the first eigenvalue of the Dirac operator on a compact Kähler spin manifold in terms of the energy momentum tensor, and an upper bound for the smallest eigenvalues of the twisted Dirac operator on Legendrian submanifolds of Sasakian manifolds. The sharpness of those estimates is also discussed.

A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.

Julián Fernández Bonder, Julio D. Rossi (2002)

Publicacions Matemàtiques

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In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end...