arXiv research

New upper bound for Neumann Laplacian eigenvalues on convex domains.

Study Hodge Laplacians for manifold data, improving error bounds.

Study eigenvalues of p-Laplacian on quaternionic Kähler manifolds.

Sharp lower bound for $p$-Laplacian eigenvalue on non-compact manifolds.

Study eigenvalues of p-Laplacian on Kähler manifolds, proving lower bounds.

Upper bounds found for eigenvalues of weighted Steklov and (p,q)-Laplacian problems.

Sharp lower bound for Hodge Laplacian on Kähler hyperbolic manifolds.

Eigenvalue estimates for Beltrami-Laplacian under specific curvature conditions.

Uniform bounds for eigenvalues of Hodge Laplacian on manifolds with lower Ricci curvature.

Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.

Extended bounds on small eigenvalues for pseudo-Laplacians on hyperbolic surfaces.

Study sets lower bounds for Kähler manifolds' Laplacian eigenvalues.

The paper analyzes graph Laplacians on manifolds with curvature bounds and applies to non-collapsed spaces.

The paper sets up eigenvalue comparison theorems for specific Laplacians on manifolds.

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…

Upper bound for Laplacian eigenvalue via conformal volume.

Uniform eigenvalue bounds for Hodge Laplacian on manifolds with Ricci curvature and injectivity radius bounds.

In this paper, we investigate the Dirchlet eigenvalue problems of poly-Laplacian with any order and quadratic polynomial operator of the Laplacian. We give some estimates for lower bounds of the sums of their first $k$ eigenvalues which improve the previous results.

Lower bound found for Kähler manifold eigenvalues.

Lower bounds for Hodge-Laplacian spectrum on orbifolds.

Study shows equality in Hodge Laplacian bound occurs only on spheres.

Graph Laplacian approximates manifold eigenvalues with controlled curvature bounds.

Paper finds lower bounds for eigenvalues of Bi-drifted Laplacian on smooth metric measure spaces.

In this paper, we investigate eigenvalues of Laplacian on a bounded domain in an $n$-dimensional Euclidean space and obtain a sharper lower bound for the sum of its eigenvalues, which gives an improvement of results due to A. D. Melas [15]. On the other hand, for the case of fractional Laplacian $(-Δ)^{α/2}|_{D}$, wher…

The paper defines new constants for $p$-Laplacian on manifolds.

The study finds bounds for the first eigenvalue of the p-Laplacian on submanifolds.

Study eigenvalues of p-Laplacian on manifolds with Robin boundary conditions.

Estimates for eigenvalues on Riemannian manifolds using classical inequalities.

Paper finds eigenvalue bounds for hyperbolic space domains.

We discuss optimal lower bounds for eigenvalues of Laplacians on weighted graphs. These bounds are formulated in terms of the geometry and, more specifically, the inradius of subsets of the graph. In particular, we study the first non-zero eigenvalue in the finite volume case and the first eigenvalue of the Dirichlet L…

We consider a complete noncompact smooth Riemannian manifold $M$ with a weighted measure and the associated drifting Laplacian. We demonstrate that whenever the $q$-Bakry-Émery Ricci tensor on $M$ is bounded below, then we can obtain an upper bound estimate for the heat kernel of the drifting Laplacian from the upper b…

We analyze the limit of the p-form Laplacian under a collapse, with bounded sectional curvature and bounded diameter, to a smooth limit space. As an application, we characterize when the p-form Laplacian has small positive eigenvalues in a collapsing sequence.

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

We give upper bounds on the eigenvalues of the differential form Laplacian on a compact Riemannian manifold. The proof uses Alexandrov spaces with curvature bounded below. We also construct differential form Laplacians on Alexandrov spaces. Under a local biLipschitz assumption on the Alexandrov space, which is conjectu…

An adapted version of the proof (due to A. Weil) of the well-known de Rham Theorem allows us to compare uniformly the spectrum of the Hodge Laplacian acting on differential forms (on a compact Riemannian manifold) to the spectrum of the combinatorial Laplacian acting on cochains associated to an open cover (made of bal…

Discrete time random walks on a finite set naturally translate via a one-to-one correspondence to discrete Laplace operators. Typically, Ollivier curvature has been investigated via random walks. We first extend the definition of Ollivier curvature to general weighted graphs and then give a strikingly simple representa…

We obtain lower bounds for the first Laplacian eigenvalues of geodesic balls of spherically symmetric manifolds. These lower bounds are only $C^{0}$ dependent on the metric coefficients.

Example surfaces with curvature bounds but no Laplacian eigenvalue lower bound.

In this paper, which is a sequel to math.DG/9902111, we analyze the limit of the p-form Laplacian under a collapse with bounded sectional curvature and bounded diameter to a singular limit space. As applications, we give results about upper and lower bounds on the j-th eigenvalue of the p-form Laplacian, in terms of se…

We give a lower bound on the number of small positive eigenvalues of the p-form Laplacian in a certain type of collapse with curvature bounded below.

The paper proves boundedness of envelopes in complex manifolds.

Improved bounds for eigenfunctions on hyperbolic surfaces found.

The paper finds lower bounds for the first eigenvalue of p-Laplacian in specific manifolds.

In this paper, we establish gradient estimates for positive solutions to the following equation with respect to the $p$-Laplacian $Δ_{p}u=-λ|u|^{p-2}u$ with $p>1$ on a given complete Riemannian manifold. Consequently, we derive upper bound estimates of the first nontrivial eigenvalue of the $p$-Laplacian.

Develops methods to analyze manifold singularities using graph Laplacian.

The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.

We prove upper bounds for sub-Laplacian eigenvalues independent of a pseudo-Hermitian structure on a CR manifold. These bounds are compatible with the Menikoff-Sjoestrand asymptotic law, and can be viewed as a CR version of Korevaar's bounds for Laplace eigenvalues of conformal metrics.

Study spectral properties of graph Laplacian for manifold data.