arXiv research

Eigenvalue estimate for shrinkers in mean curvature flow.

The paper compares Steklov and Laplacian eigenvalues on graphs.

Paper finds a graph Steklov eigenvalue estimate with rigidity results.

Eigenvalue estimates for weighted manifolds with applications.

The paper provides estimates for eigenvalues of elliptic differential problems.

New biharmonic Steklov problem on forms yields eigenvalue estimates.

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

The paper studies eigenvalue problems on manifolds and recovers known inequalities.

Paper finds how Steklov eigenvalues change on graphs and trees.

New eigenvalue estimate for CR manifolds' Kohn-Dirac operator.

In study of eigenvalue problems, a classical problem is the Stekloff eigenvalue problem. There are many estimates of the first non- zero Stekloff eigenvalue, including a sharp estimate on surfaces, obtained by Escobar in "The geometry of the first non-zero Stekloff eigenvalue, J. Funct. Anal. 150 (1997)". In this paper…

The paper improves eigenvalue estimates for manifolds with Ricci curvature conditions.

Estimates for eigenvalues on Riemannian manifolds using classical inequalities.

Lower bounds for eigenvalues on Bakry-Emery manifolds proven.

Paper extends Steklov eigenvalue estimate to weighted graphs.

Estimates small eigenvalues for geometrically finite manifolds.

For an $n$-dimensional compact submanifold $M^n$ in the Euclidean space $\mathbf R^{N}$, we study estimates for eigenvalues of the Paneitz operator on $M^n$. Our estimates for eigenvalues are sharp.

The paper explores inequalities between eigenvalues on Riemannian manifolds.

In this paper, we study eigenvalues of the closed eigenvalue problem of the differential operator $L$, which is introduced by Colding and Minicozzi in [4], on an $n$-dimensional compact self-shrinker in ${R}^{n+p}$. Estimates for eigenvalues of the differential operator $L$ are obtained. Our estimates for eigenvalues…

The paper estimates eigenvalues for specific differential operators on curved spaces.

Estimates eigenvalues and spectrum for graph substructures using isocapacitary constants.

Estimates eigenvalues on weighted manifolds with curvature.

Estimates eigenvalue for Hermitian manifolds using curvature.

In this paper, we derive the CR Reilly's formula and its applications to studying of the first eigenvalue estimate for CR Dirichlet eigenvalue problem and embedded p-minimal hypersurfaces. In particular, we obtain the first Dirichlet eigenvalue estimate in a compact pseudohermitian (2n+1)-manifold with boundary and the…

In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].

In this paper, motivated by the work of Raulot and Savo, we generalize Raulot-Savo's estimate for the first Steklov eigenvalues of Euclidean domains to higher Steklov eigenvalues.

Study eigenvalue estimates on Kähler and quaternion Kähler manifolds.

In this paper, we study Lichnerowicz type estimate for eigenvalues of drifting Laplacian operator and L1 and L2 energy for drifting heat equation on closed manifolds with weighted measure. In some sense, this study is about the eigenvalue estimate on Ricci solitons.

Study on stability of quaternion-Kähler manifolds using eigenvalue estimates.

In this paper, we consider lower order eigenvalues of Laplacian operator with any order in Euclidean domains. By choosing special rectangular coordinates, we obtain two estimates for lower order eigenvalues.

Estimates gaps between eigenvalues for elliptic operators on manifolds.

The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.

The paper provides estimates for Steklov eigenvalues of surfaces with boundary.

In this paper, we extend the Reilly formula for drifting Laplacian operator and apply it to study eigenvalue estimate for drifting Laplacian operators on compact Riemannian manifolds boundary. Our results on eigenvalue estimates extend previous results of Reilly and Choi and Wang.

Estimates for plate eigenvalues with nonzero Poisson's ratio.

Proves rigidity for eigenvalue estimate on three-manifolds.

Sharp Steklov eigenvalue estimates for differential forms on manifolds.

We consider the higher order buckling eigenvalues of the following Dirichlet poly-Laplacian in the unit sphere $(-Δ)^p u=Λ(-Δ) u$ with order $p(\geq2)$. We obtain universal bounds on the $(k+1)$th eigenvalue in terms of the first $k$th eigenvalues independent of the domains. In particular, for $p=2$, our result is shar…

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…

In this note, we obtain the sharp estimates for the first eigenvalue of Paneitz operator for $4$-dimensional compact submanifolds in Euclidean space. Since unit spheres and projective spaces can be canonically imbedded into Euclidean space, the corresponding estimates for the first eigenvalue are also obtained.

We prove Li-Yau-Kröger type bounds for Neumann-type eigenvalues of the poly-harmonic operator and of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a biharmonic Steklov problem and of the Laplacian, which directly implies two sharp Reilly-ty…

Gradient and eigenvalue estimates for Kähler manifolds' canonical bundle.

In this paper, we consider an eigenvalue problem of the elliptic operator $L_r={\rm div}(T^r\nabla\cdot )$ on compact submanifolds in arbitrary codimension of space forms $\mathbb{R}^N(c)$ with $c\geq0$. Our estimates on eigenvalues are sharp.

Estimates the first eigenvalue of a Schrödinger operator on minimal submanifolds.

Estimates the first eigenvalue for embedded hypersurfaces in manifolds with Ricci curvature bounds.

We give some sharp lower bounds of the first eigenvalue for the Hodge Laplacian acting on differential forms on the boundary of a Riemannian manifold. We also give some sharp estimates for the first nonzero Steklov eigenvalue for differential forms.

Study on biharmonic Steklov problems with Neumann boundary conditions and eigenvalue estimates.

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…