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New Universal Inequalities for Eigenvalues of a Clamped Plate Problem
In this paper, we study the universal inequalities for eigenvalues of a clamped plate problem, and establish some new universal inequalities that are...
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New Bounds on Eigenvualues of Laplacian
In this paper, we investigate non-zero positive eigenvalues of the Laplacian with Dirichlet boundary condition in an n -dimentional Euclidean space ℝ n ,...
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Nodal Sets of Laplace Eigenfunctions: Estimates of the Hausdorff Measure in Dimensions Two and Three
Let ΔM be the Laplace operator on a compact n-dimensional Riemannian manifold without boundary. We study the zero sets of its eigenfunctions u :...
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Estimates for eigenvalues of fourth-order elliptic operators in divergence form
In this paper, we study the eigenvalue problem of fourth-order elliptic operators in divergence form with weight on compact Riemannian manifolds with...
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Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds
For a compact Riemannian manifold M immersed into a higher dimensional manifold which can be chosen to be a Euclidean space, a unit sphere, or even a...
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A spinorial characterization of hyperspheres
Let M be a compact orientable n -dimensional hypersurface, with nowhere vanishing mean curvature H , immersed in a Riemannian spin manifold
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Pseudodifferential Operators on Manifolds: A Coordinate-free Approach
The main aim of the paper is to demonstrate the advantage of a coordinate-free approach to the theory of pseudodifferential operators. We explain how...
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Inequalities for eigenvalues of a clamped plate problem
In this paper we study eigenvalues of a clamped plate problem on compact domains in complete manifolds. For complete manifolds admitting special...
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Estimates for lower order eigenvalues of a clamped plate problem
For a bounded domain Ω in a complete Riemannian manifold M n , we study estimates for lower order eigenvalues of a clamped plate problem. We obtain...
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Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds
In this paper, we study eigenvalues of elliptic operators in divergence form on compact Riemannian manifolds with boundary (possibly empty) and...
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Estimates for eigenvalues of the poly-Laplacian with any order in a unit sphere
In this paper we study eigenvalues of the poly-Laplacian with any order on a domain in an n -dimensional unit sphere and obtain estimates for...
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Three Topological Properties of Small Eigenfunctions on Hyperbolic Surfaces
We apply topological methods for studying eigenfunctions on finite volume hyperbolic surfaces. From the Lemma saying that any non-zero eigenfunction...
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Bounds on eigenvalues of Dirichlet Laplacian
In this paper, we investigate an eigenvalue problem of Dirichlet Laplacian on a bounded domain Ω in an n -dimensional Euclidean space R ...
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Eigenvalues of the basic Dirac operator on quaternion-Kähler foliations
In this paper, we give an optimal lower bound for the eigenvalues of the basic Dirac operator on a quaternion-Kähler foliations. The limiting case is...
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Curvature bounds for the spectrum of a compact Riemannian manifold of constant scalar curvature
Let (M, g) be an n-dimensional compact and connected Riemannian manifold of constant scalar curvature. If the sectional curvatures of M are bounded...
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Statistical Inverse Problems on Manifolds
This article examines statistical inverse problems on compact Riemannian manifolds. The approach is to use aspects of spectral geometry associated...
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Estimates on Eigenvalues of Laplacian
In this paper, we study eigenvalues of Laplacian on either a bounded connected domain in an n -dimensional unit sphere S n (1), or a compact...