1 citations · 3 across the 14 of their papers we have counts for
14 papers
The First Eigenvalue of Embedded Minimal Hypersurfaces in the Unit Sphere I: Yau's Conjecture
Lingzhong Zeng
In this paper, by meticulously constructing a minimizing sequence within a suitable Sobolev space and leveraging the variational principle, we establish that the first non-zero eig…
Spectrum of the Dirac operator on Compact Riemannian Manifolds
Lingzhong Zeng
In this paper, we consider the eigenvalue problem of Dirac operator on a compact Riemannian manifold isometrically immersed into Euclidean space and derive some extrinsic estimates…
Universal Bounds for Fractional Laplacian on a Bounded Open Domain in
Lingzhong Zeng
Let be a bounded open domain on the Euclidean space and be the set of all positive rational numbers. In 2017, Chen and Zeng investigated the e…
Eigenvalues for the Clamped Plate Problem of Operator on Complete Riemannian manifolds
Lingzhong Zeng
operator is an important extrinsic differential operator of divergence type and has profound geometric settings. In this paper, we consider the clamped plate probl…
Eigenvalue Inequalities for the Clamped Plate Problem of Operator
Lingzhong Zeng
operator is introduced by Y.-L. Xin (\emph{Calculus of Variations and Partial Differential Equations. 2015, \textbf{54}(2):1995-2016)}, which is an important ex…
Eigenvalues of Xin-Laplacian on Complete Riemannian manifolds
Lingzhong Zeng, Zhouyuan Zeng
In this paper, we firstly consider Dirichlet eigenvalue problem which is related to Xin-Laplacian on the bounded domain of complete Riemannian manifolds. By establishing the genera…
The First Eigenvalue for the Bi-Beltrami-Laplacian on Minimal Isoparametric Hypersurfaces of
Lingzhong Zeng
In this paper, we investigate the first eigenvalues of two closed eigenvalue problems of the bi-Beltrami-Laplacian on minimal embedded isoparametric hypersurface in the unit sphere…
The Gap of the Consecutive Eigenvalues of the Drifting Laplacian on Metric Measure Spaces
Lingzhong Zeng
In this paper, we investigate eigenvalues of the Dirichlet problem and the closed eigenvalue problem of drifting Laplacian on the complete metric measure spaces and establish the c…
The Gaps of Consecutive Eigenvalues of Laplacian on Riemannian Manifolds
Lingzhong Zeng
In this paper, we investigate the Dirichlet problem of Laplacian on complete Riemannian manifolds. By constructing new trial functions, we obtain a sharp upper bound of the gap of…
Upper Bound Estimates for Eigenvalues of the Poly-Laplacian
Lingzhong Zeng
In this paper, we obtain a sharp upper bound for the sum of the first -th eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which is viewed as an extensio…
Eigenvalues of the Witten-Laplacian on compact Riemannian manifolds
Qing-Ming Cheng, Lingzhong Zeng
In this paper we study eigenvalues of the closed eigenvalue problem of the Witten-Laplacian on an -dimensional compact Riemannian manifold. Estimates for eigenvalues are given.…
Estimates for Eigenvalues of Poly-harmonic Operators
Guoxin Wei, Lingzhong Zeng
In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an n-dimensional Euclidean space and obtain a lower bound for eigenvalues, whi…
Estimates for lower bounds of eigenvalues of the poly-Laplacian and quadratic polynomial operator of the Laplacian
Qing-Ming Cheng, He-Jun Sun, Guoxin Wei +1
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…
Lower Bounds for Laplacian and Fractional Laplacian Eigenvalues
Guoxin Wei, He-Jun Sun, Lingzhong Zeng
In this paper, we investigate eigenvalues of Laplacian on a bounded domain in an -dimensional Euclidean space and obtain a sharper lower bound for the sum of its eigenvalues, wh…