arXiv research

In this paper, we investigate universal estimates for eigenvalues of a buckling problem. For a bounded domain in a Euclidean space, we give a positive contribution for obtaining a sharp universal inequality for eigenvalues of the buckling problem. For a domain in the unit sphere, we give an important improvement on the…

We discuss the decomposition of the zeta-determinant of the square of the Dirac operator into contributions coming from the different parts of the manifold. The easy case was worked in the previous paper of authors. Due to the assumptions made on the operators in the previous paper, we were able to avoid the presence o…

Unified treatment of eigenvalue processes using Riemannian geometry.

We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special structure superimposed due to the time-shift. We demonstrate that the associated eigen…

Paper studies eigenvalues of a specific operator on Riemannian manifolds.

New bounds on KPCA efficiency reveal conditions for fast convergence.

Upper bounds for second Robin eigenvalue on Riemannian surfaces.

New insights into hidden minima in neural networks.

CoPhy-PGNN tackles competing PG losses in neural networks for solving eigenvalue problems.

We consider the $SL(2,R)$ action on moduli spaces of quadratic differentials. If $μ$ is an $SL(2,R)$-invariant probability measure, crucial information about the associated representation on $L^2(μ)$ (and in particular, fine asymptotics for decay of correlations of the diagonal action, the Teichmüller flow) is encoded …

Study finds topological restrictions for stable free boundary CMC surfaces in negatively curved settings.

In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling price fluctuations as GARCH(1,1) process. The corresponding correlation matrix is constructed. It is found that the distribut…

We discuss a peculiar interplay between the representation theory of the holonomy group of a Riemannian manifold, the Weitzenboeck formula for the Hodge-Laplace operator on forms and the Lichnerowicz formula for twisted Dirac operators. For quaternionic Kaehler manifolds this leads to simple proofs of eigenvalue estima…

We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.

Stability of Morse index for harmonic maps on degenerating surfaces analyzed.

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the specific kernel ridge regression setup, a simple distance-based test statistic is prop…

This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…

The paper compares Steklov and Laplacian eigenvalues on graphs.

We study the singularities of the exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues of the curvature tensor, and their contribution to the Maslov index of the geodesic is computed explicitly. We prove that degeneracy of conjugate po…

In this paper, two interesting eigenvalue comparison theorems for the first non-zero Steklov eigenvalue of the Laplacian have been established for manifolds with radial sectional curvature bounded from above. Besides, sharper bounds for the first non-zero eigenvalue of the Wentzell eigenvalue problem of the weighted La…

The paper explores inequalities between eigenvalues on Riemannian manifolds.

Novel model captures high-dimensional copulas with spectral dynamics and regularization.

Eigenvalues of Steklov eigenproblems change predictably with boundary tweaks.

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

The paper sets lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.

Paper finds how Steklov eigenvalues change on graphs and trees.

Eigenvalue estimate for shrinkers in mean curvature flow.

In this paper we study eigenvalues of the closed eigenvalue problem of the Witten-Laplacian on an $n$-dimensional compact Riemannian manifold. Estimates for eigenvalues are given. As applications, we give a sharp upper bound for the $k^{\text{th}}$ eigenvalue and for isoparametric minimal hypersurfaces in the unit sphe…

For a bounded domain $Ω$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Lap…

The paper provides estimates for eigenvalues of elliptic differential problems.

The paper compares eigenvalues of Dirichlet, Neumann, and Laplacian on graphs.

Sharp bounds derived for the first two Steklov eigenvalues of exterior domains.

Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &Δ{\mathbf u}+ α{\rm grad}(\text{div}{\mathbf u})=-σ{\mathbf u}, \ \text{in $Ω$}, &{\mathbf u}|_{\partial Ω}={\mathbf 0}. \aligned . $$ Estimate…

Krein's formula for conic Laplacians on compact Riemann surfaces

Improved lower bounds for poly-Laplacian eigenvalues in arbitrary dimensions.

Study eigenvalues of p-Laplacian on quaternionic Kähler manifolds.

We study the eigenvalue problem for the Riemannian Pucci operator on geodesic balls. We establish upper and lower bounds for the principal Pucci eigenvalues depending on the curvature, extending Cheng's eigenvalue comparison theorem for the Laplace-Beltrami operator. For manifolds with bounded sectional curvature, we p…

The paper studies eigenvalues of Xin-Laplacian on Riemannian manifolds.

The paper finds new inequalities for Laplacian and biharmonic eigenvalues on manifolds.

In this paper, we mainly study eigenvalue problems of p-Laplacian on domains with an interior hole. Firstly we prove Faber-Krahn-type inequalities, and Cheng-type eigenvalue comparison theorems on manifolds. Secondly, we prove a comparison theorem for eigenvalues with inner Dirichlet and outer Neumann boundary in minim…

Study on eigenvalues of complex Hessian operator on pseudoconvex manifolds.

Study on second Robin eigenvalue for Laplacian on manifolds.

Paper finds principal eigenvalue for infinity Laplacian in metric spaces.

Estimates for eigenvalues on Riemannian manifolds using classical inequalities.

Lower bounds for eigenvalues on Bakry-Emery manifolds proven.

Study proves inequalities for eigenvalues of fourth-order elliptic operators on Riemannian manifolds.

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.

Continuing our previous work (arXiv:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on finite or locally finite graphs. In general, the gradient estimate in the present paper is independent of our previous one. As applications, i…