Eigenvalues of the Laplacian and curvature
Kornel Benko, Monika Kothe, Klaus-Dieter Semmler, Udo Simon (1979)
Colloquium Mathematicae
Similarity:
Displaying similar documents to “A minorization of the first positive eigenvalue of the scalar laplacian on a compact Riemannian manifold”
Eigenvalues of the Laplacian and curvature
Compact Kaehler manifolds and the eigenvalues of the Laplacian
Seiichi Udagawa (1988)
Colloquium Mathematicae
Similarity:
An integro-differential inequality related to the smallest positive eigenvalue ofp(x)-Laplacian Dirichlet problem
Damian Wiśniewski, Mariusz Bodzioch (2016)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Similarity:
We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
Equality in Wielandt’s eigenvalue inequality
Shmuel Friedland (2015)
Special Matrices
Similarity:
In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.
The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
Hajime Urakawa (1986)
Compositio Mathematica
Similarity:
Dependence of a differential equation on the first eigenvalue of a suitable problem
Jan Bochenek (1980)
Annales Polonici Mathematici
Similarity:
Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian
Kei Funano (2016)
Analysis and Geometry in Metric Spaces
Similarity:
We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.
A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
Julián Fernández Bonder, Julio D. Rossi (2002)
Publicacions Matemàtiques
Similarity:
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...
On the spectrum of Riemannian submersions with totally geodesic fibers
Gérard Besson, Manlio Bordoni (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Similarity:
In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.
On some properties of eigenvalues and eigenfunctions of certain differential equations of the fourth order
Jan Bochenek (1971)
Annales Polonici Mathematici
Similarity:
On a lower bound of the second eigenvalue of the Laplacian on an Einstein space
Shukichi Tanno (1978)
Colloquium Mathematicae
Similarity:
A Note on the First Nonzero Eigenvalue of the Laplacian Acting of P-Forms.
Gilles Courtois, Bruno Colbois (1990)
Manuscripta mathematica
Similarity:
Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string
Behrouz Emamizadeh, Amin Farjudian (2014)
Nonautonomous Dynamical Systems
Similarity:
In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will...