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Manifolds with Density and the First Steklov Eigenvalue
There are many interesting eigenvalue problems in a variety of settings; one of them is the well-known Steklov eigenvalue problem. In this work, we...
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Lower Bounds for the First Eigenvalue of the p-Laplacian on Quaternionic Kähler Manifolds
We study the first nonzero eigenvalues for the p -Laplacian on quaternionic Kähler manifolds. Our first result is a lower bound for the first nonzero...
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A monotonicity result for the first Steklov–Dirichlet Laplacian eigenvalue
In this paper, we consider the first Steklov–Dirichlet eigenvalue of the Laplace operator in annular domains with a spherical hole. We prove a...
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Non-monotonicity of the first eigenvalue for the 3D magnetic Robin Laplacian
Previous works provided several counterexamples to monotonicity of the lowest eigenvalue for the magnetic Laplacian in the two-dimensional case....
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Estimates for the first eigenvalue of diffusion-type operators in weighted manifolds
We provide several lower bounds for the first eigenvalue for some classical eigenvalue problems with respect to the diffusion-type operator
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Optimization of the First Dirichlet Laplacian Eigenvalue with Respect to a Union of Balls
The problem of minimizing the first eigenvalue of the Dirichlet Laplacian with respect to a union of m balls with fixed identical radii and variable...
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The First Eigenvalue for Nonlocal Operators
In this chapter we present some results concerning the first eigenvalue for a nonlocal operator in convolution form with a smooth kernel. Given a...
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Variation of the first eigenvalue of Witten Laplacian and consequences under super Perelman-Ricci flow
This paper is concerned with variation formula for the first eigenvalue of Witten-Laplacian on closed smooth metric measure spaces evolving by a...
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The Obata First Eigenvalue Theorem on a Seven-Dimensional Quaternionic Contact Manifold
We prove an Obata type rigidity result for the first eigenvalue of the sub-Laplacian on a compact seven-dimensional quaternionic contact manifold...
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First Dirichlet Eigenvalue and Exit Time Moments: A Survey
In this paper we summarize recent results concerning the connection between the...
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On the second Robin eigenvalue of the Laplacian
We study the Robin eigenvalue problem for the Laplace–Beltrami operator on Riemannian manifolds. Our first result is a comparison theorem for the...
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Eigenvalue Problems
One of the central problems considered in this chapter is: given an \(n \times n\)...
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Introduction to Eigenvalue Problems
This chapter provides an overview of the literature concerning explicit eigenvalue bounds achieved through numerical methods. It outlines the rapid...
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The First Eigenvalue of a Homogeneous CROSS
We provide explicit formulae for the first eigenvalue of the Laplace–Beltrami operator on a compact rank one symmetric space (CROSS) endowed with any...
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The Maximization of the First Eigenvalue for a Two-Phase Material
We study the optimal arrangement of two conductive materials in order to maximize the first eigenvalue of the corresponding diffusion operator with...
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Estimates for Variation of the First Dirichlet Eigenvalue of the Laplace Operator
We obtain an estimate for variation of the first eigenvalue of the Laplace operator with the Dirichlet boundary condition in a bounded domain. The...