Proceedings of the London Mathematical Society, ISSN 0024-6115, 05/2020, Volume 120, Issue 5, pp. 704 - 741

We study the smallest positive eigenvalue λ1(M) of the Laplace–Beltrami operator on a closed hyperbolic 3‐manifold M which fibers over the circle, with fiber a...

30F60 (primary) | 20P05 (secondary) | 58C40 | MATHEMATICS | DISTANCE | COMPLEX | VOLUMES | BOUNDS | CLASSIFICATION | KLEINIAN SURFACE GROUPS | GEODESICS | GEOMETRY

30F60 (primary) | 20P05 (secondary) | 58C40 | MATHEMATICS | DISTANCE | COMPLEX | VOLUMES | BOUNDS | CLASSIFICATION | KLEINIAN SURFACE GROUPS | GEODESICS | GEOMETRY

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 10/2017, Volume 17, Issue 4, pp. 781 - 792

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 11/2017, Volume 290, Issue 16, pp. 2708 - 2713

Recently, Andrews and Clutterbuck [1] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat...

eigenvalue estimates | Ricci curvature | Eigenfunctions | 58C40 | 35P15 | maximum principle

eigenvalue estimates | Ricci curvature | Eigenfunctions | 58C40 | 35P15 | maximum principle

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 06/2017, Volume 95, Issue 3, pp. 763 - 784

We use layer potential to establish that the boundary biharmonic Steklov operators are elliptic pseudo‐differential operators. Thus we are able to establish...

58J50 (primary) | 58C40 | MATHEMATICS | EIGENVALUES | HAUSDORFF MEASURE | INEQUALITIES | EIGENFUNCTIONS | RIEMANNIAN-MANIFOLDS | SURFACES

58J50 (primary) | 58C40 | MATHEMATICS | EIGENVALUES | HAUSDORFF MEASURE | INEQUALITIES | EIGENFUNCTIONS | RIEMANNIAN-MANIFOLDS | SURFACES

Journal Article

Mathematische Annalen, ISSN 0025-5831, 10/2012, Volume 354, Issue 2, pp. 451 - 463

In this paper, we first derive a monotonicity formula for the first eigenvalue of $${-\Delta +aR (0 < a \leq 1/2)}$$ on a closed surface with nonnegative...

Secondary 58C40 | Mathematics, general | Mathematics | Primary 53C44 | LAPLACIAN | MATHEMATICS | FUNCTIONALS

Secondary 58C40 | Mathematics, general | Mathematics | Primary 53C44 | LAPLACIAN | MATHEMATICS | FUNCTIONALS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2019, Volume 2019, Issue 1, pp. 1 - 16

Let Δp,ϕ $\Delta _{p,\phi }$ be the weighted p-Laplacian defined on a smooth metric measure space. We study the evolution and monotonicity formulas for the...

Analysis | 53C44 | 53C21 | Eigenvalue | Mathematics, general | 58C40 | Mathematics | Ricci solitons | Applications of Mathematics | Ricci harmonic flow | Monotonicity | Laplace-Beltrami operator | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION | GEOMETRIC OPERATORS | Eigenvalues | Eigen values

Analysis | 53C44 | 53C21 | Eigenvalue | Mathematics, general | 58C40 | Mathematics | Ricci solitons | Applications of Mathematics | Ricci harmonic flow | Monotonicity | Laplace-Beltrami operator | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION | GEOMETRIC OPERATORS | Eigenvalues | Eigen values

Journal Article

Journal of Differential Geometry, ISSN 0022-040X, 05/2013, Volume 94, Issue 1, pp. 1 - 58

We prove a surgery formula for the smooth Yamabe invariant sigma(M) of a compact manifold M. Assume that N is obtained from M by surgery of codimension at...

MATHEMATICS | RP3 | GREATER-THAN | SIMPLY CONNECTED MANIFOLDS | METRICS | 3-MANIFOLDS | POSITIVE SCALAR CURVATURE | CLASSIFICATION | 4-MANIFOLDS | RIEMANNIAN-MANIFOLDS

MATHEMATICS | RP3 | GREATER-THAN | SIMPLY CONNECTED MANIFOLDS | METRICS | 3-MANIFOLDS | POSITIVE SCALAR CURVATURE | CLASSIFICATION | 4-MANIFOLDS | RIEMANNIAN-MANIFOLDS

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 3/2010, Volume 37, Issue 3, pp. 345 - 361

The paper is concerned with the local and global bifurcation structure of positive solutions $${u,v\in H^1_0(\Omega)}$$ of the system...

35B05 | 35J50 | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Analysis | 35B32 | 58C40 | Mathematics | 58E07 | 35J55 | MATHEMATICS | COUPLED SCHRODINGER-EQUATIONS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | R-N | STATES | SOLITARY WAVES | ANNULUS | SPIKES | POTENTIALS | UNIQUENESS | Mathematical analysis | Bifurcations | Nonlinearity | Bifurcation theory | Joining | Schroedinger equation | Spectra | Nonlinear optics

35B05 | 35J50 | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Analysis | 35B32 | 58C40 | Mathematics | 58E07 | 35J55 | MATHEMATICS | COUPLED SCHRODINGER-EQUATIONS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | R-N | STATES | SOLITARY WAVES | ANNULUS | SPIKES | POTENTIALS | UNIQUENESS | Mathematical analysis | Bifurcations | Nonlinearity | Bifurcation theory | Joining | Schroedinger equation | Spectra | Nonlinear optics

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2018, Volume 15, Issue 2, pp. 1 - 20

In this paper, we study monotonicity formulas of eigenvalues of Laplacian and entropies along the rescaled List’s extended Ricci flow, which is a weakly...

eigenvalues | 53C44 | Mathematics, general | 58C40 | Mathematics | monotonicity | List’s extended Ricci flow

eigenvalues | 53C44 | Mathematics, general | 58C40 | Mathematics | monotonicity | List’s extended Ricci flow

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 07/2019, Volume 44, Issue 7, pp. 573 - 612

We consider the first non-zero eigenvalue λ 1 of the Laplacian on hyperbolic surfaces for which one disconnecting collar degenerates and prove that essentially...

degenerating hyperbolic surfaces | eigenvalues of Laplacian | Asymptotic estimates | 58C40 | 30F10 | MATHEMATICS | MATHEMATICS, APPLIED | BEHAVIOR | GEODESIC-LENGTH FUNCTIONS | METRICS | RIEMANN SURFACES | ASYMPTOTICS | FLOW | Eigenvalues | Eigen values

degenerating hyperbolic surfaces | eigenvalues of Laplacian | Asymptotic estimates | 58C40 | 30F10 | MATHEMATICS | MATHEMATICS, APPLIED | BEHAVIOR | GEODESIC-LENGTH FUNCTIONS | METRICS | RIEMANN SURFACES | ASYMPTOTICS | FLOW | Eigenvalues | Eigen values

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 10/2019, Volume 81, Issue 1, pp. 252 - 270

Recently, a class of eigensolvers based on contour integrals has been developed for computing the eigenvalues inside a given region in the complex plane. The...

Generalized eigenvalue problems | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | QZ method | Mathematical and Computational Engineering | Contour integral | 58C40 | 65F15 | Mathematics | Generalized Schur decomposition | 15A18 | PROJECTION | MATHEMATICS, APPLIED | FEAST ALGORITHM | EIGENSOLVER

Generalized eigenvalue problems | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | QZ method | Mathematical and Computational Engineering | Contour integral | 58C40 | 65F15 | Mathematics | Generalized Schur decomposition | 15A18 | PROJECTION | MATHEMATICS, APPLIED | FEAST ALGORITHM | EIGENSOLVER

Journal Article

Mathematical Programming, ISSN 0025-5610, 11/2019, Volume 178, Issue 1, pp. 215 - 262

The problem of optimizing a quadratic form over an orthogonality constraint (QP-OC for short) is one of the most fundamental matrix optimization problems and...

58C05 | 65K05 | Quadratic optimization with orthogonality constraints | Theoretical, Mathematical and Computational Physics | Mathematics | 90C26 | Łojasiewicz inequality | Mathematical Methods in Physics | Linear convergence | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 15B10 | 58C40 | Stochastic variance-reduced gradient method | Combinatorics | Line-search methods | MATHEMATICS, APPLIED | POWER METHOD | INEQUALITIES | DESCENT METHODS | ALGORITHMS | SUMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATRICES | FRAMEWORK | ojasiewicz inequality | SYSTEMS | ERROR-BOUNDS | FLOWS | Quadratic forms | Critical point | Iterative methods | Orthogonality | Manifolds (mathematics) | Optimization | Convergence | Algorithms

58C05 | 65K05 | Quadratic optimization with orthogonality constraints | Theoretical, Mathematical and Computational Physics | Mathematics | 90C26 | Łojasiewicz inequality | Mathematical Methods in Physics | Linear convergence | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 15B10 | 58C40 | Stochastic variance-reduced gradient method | Combinatorics | Line-search methods | MATHEMATICS, APPLIED | POWER METHOD | INEQUALITIES | DESCENT METHODS | ALGORITHMS | SUMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATRICES | FRAMEWORK | ojasiewicz inequality | SYSTEMS | ERROR-BOUNDS | FLOWS | Quadratic forms | Critical point | Iterative methods | Orthogonality | Manifolds (mathematics) | Optimization | Convergence | Algorithms

Journal Article

13.
Full Text
Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound

Mathematische Zeitschrift, ISSN 0025-5874, 2014, Volume 277, Issue 3-4, pp. 867 - 891

We complete the picture of sharp eigenvalue estimates for the -Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of...

MATHEMATICS

MATHEMATICS

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 02/2016, Volume 81, Issue 2, pp. 167 - 207

We develop a nonlinear spectral graph theory, in which the Laplace operator is replaced by the 1 − Laplacian Δ1. The eigenvalue problem is to solve a nonlinear...

05C75 | 58E05 | critical point theory | 05C50 | Cheeger's constant | 58C40 | 1‐Laplace operator | 05C35 | spectral graph theory | 1-Laplace operator | MATHEMATICS

05C75 | 58E05 | critical point theory | 05C50 | Cheeger's constant | 58C40 | 1‐Laplace operator | 05C35 | spectral graph theory | 1-Laplace operator | MATHEMATICS

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 3/2019, Volume 78, Issue 3, pp. 1942 - 1961

In many applications, the information about the number of eigenvalues inside a given region is required. In this work, we develop a contour-integral based...

Generalized eigenvalue problem | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Contour integral | Eigenvalue | 58C40 | 65F15 | Mathematics | Spectral projection | 15A18 | MATHEMATICS, APPLIED | ALGORITHM

Generalized eigenvalue problem | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Contour integral | Eigenvalue | 58C40 | 65F15 | Mathematics | Spectral projection | 15A18 | MATHEMATICS, APPLIED | ALGORITHM

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 01/2019, Volume 67, Issue 1, pp. 186 - 195

We consider the algebra of mixed multidimensional integral operators. In particular, Fredholm integral operators belong to this algebra. For the piecewise...

Operator algebras | traces and determinants | representation of integral operators | piecewise constant kernel functions | 16G99 | 45P05 | 47G10 | 58C40 | 74J05 | MATHEMATICS | PERIODIC OPERATORS | ALGEBRA | Kernels | Operators (mathematics) | Algebra | Representations | Integrals

Operator algebras | traces and determinants | representation of integral operators | piecewise constant kernel functions | 16G99 | 45P05 | 47G10 | 58C40 | 74J05 | MATHEMATICS | PERIODIC OPERATORS | ALGEBRA | Kernels | Operators (mathematics) | Algebra | Representations | Integrals

Journal Article

manuscripta mathematica, ISSN 0025-2611, 7/2019, Volume 159, Issue 3, pp. 453 - 473

On a two-dimensional compact Riemannian manifold with boundary, we prove that the first nonzero Steklov eigenvalue is nondecreasing along the unnormalized...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53C44 | 58J50 | Mathematics, general | Algebraic Geometry | 58C40 | Mathematics | Number Theory

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53C44 | 58J50 | Mathematics, general | Algebraic Geometry | 58C40 | Mathematics | Number Theory

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2018, Volume 290, Issue 3, pp. 1115 - 1143

A classical question in spectral geometry is, for each pair of nonnegative integers (p, n) such that $$p\le 2n$$ p≤2n , if the eigenvalues of the Laplacian on...

Volume | 53C55 | 58J50 | Mathematics, general | 58C40 | Mathematics | Rigidity | Complex projective space | Fano Kähler–Einstein manifold | Spectrum | LAPLACIAN | MATHEMATICS | Fano Kahler-Einstein manifold | KAHLER | MANIFOLDS | UNIQUENESS

Volume | 53C55 | 58J50 | Mathematics, general | 58C40 | Mathematics | Rigidity | Complex projective space | Fano Kähler–Einstein manifold | Spectrum | LAPLACIAN | MATHEMATICS | Fano Kahler-Einstein manifold | KAHLER | MANIFOLDS | UNIQUENESS

Journal Article

Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 06/2019, Volume 27, Issue 2, pp. 179 - 211

We set out to obtain estimates of the Laplacian Spectrum of Riemannian manifolds with non-empty boundary. This was achieved using standard doubled manifold...

Primary 35P15 53C20 | Secondary 53C21 58C40 | Regularized metric with control of curvature | Double of a manifold | Topological invariants | Laplacian | VIBRATION FREQUENCIES | MATHEMATICS | MATHEMATICS, APPLIED

Primary 35P15 53C20 | Secondary 53C21 58C40 | Regularized metric with control of curvature | Double of a manifold | Topological invariants | Laplacian | VIBRATION FREQUENCIES | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Mathematische Annalen, ISSN 0025-5831, 8/2016, Volume 365, Issue 3, pp. 1603 - 1632

We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion...

Primary 58C40 | Secondary 53C20 | Mathematics, general | Mathematics | LAPLACIAN | MATHEMATICS | COMPACT | DOMAIN | SUBMANIFOLDS | INEQUALITIES | BOUNDS | CURVATURE | TORSIONAL RIGIDITY

Primary 58C40 | Secondary 53C20 | Mathematics, general | Mathematics | LAPLACIAN | MATHEMATICS | COMPACT | DOMAIN | SUBMANIFOLDS | INEQUALITIES | BOUNDS | CURVATURE | TORSIONAL RIGIDITY

Journal Article

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