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    Bornes supérieures pour les valeurs propres des opérateurs naturels sur des variétés riemanniennes compactes

    Hassannezhad, Asma
    Neuchâtel : Université de Neuchâtel, Faculté des sciences
    2012
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    Titre: Bornes supérieures pour les valeurs propres des opérateurs naturels sur des variétés riemanniennes compactes / Asma Hassannezhad
    Auteur: Hassannezhad, Asma
    Editeur: Neuchâtel : Université de Neuchâtel, Faculté des sciences
    Date: 2012
    Collation: 70 p. ; 30 cm
    Sujet RERO: Riemann, Variétés de - Schrödinger, Opérateur de - Laplacien - Valeurs propres
    Note: Introduction en français et en anglais. - Thèse Université de Neuchâtel, 2012 - Existe aussi en version électronique
    No RERO: R007166475
    Existe sous différentes formes: Bornes supérieures pour les valeurs propres des opérateurs naturels sur des variétés riemanniennes compactes
    Permalien:
    http://data.rero.ch/01-R007166475/html

    • Article
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    Eigenvalues of the Laplacian and extrinsic geometry

    Hassannezhad, Asma
    Annals of Global Analysis and Geometry. - 2013/44/4/517-527
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    Aucune localisation rattachée
    Titre: Eigenvalues of the Laplacian and extrinsic geometry
    Auteur: Hassannezhad, Asma
    Sujet: Laplacian - Eigenvalue - Upper bound - Intersection index
    Description: We extend the results given by Colbois, Dryden and El Soufi on the relationships between the eigenvalues of the Laplacian and an extrinsic invariant called intersection index, in two directions. First, we replace this intersection index by invariants of the same nature which are stable under small perturbations. Second, we consider complex submanifolds of the complex projective space $$\mathbb C P^N$$ C P N instead of submanifolds of $$\mathbb R ^N$$ R N and we obtain an eigenvalue upper bound depending only on the dimension of the submanifold which is sharp for the first non-zero eigenvalue
    Publication en relation: Annals of Global Analysis and Geometry. - 2013/44/4/517-527
    Document hôte: Annals of Global Analysis and Geometry
    Identifiant: 10.1007/s10455-013-9379-8 (DOI)

    • Article
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    Eigenvalues of the Laplacian and extrinsic geometry

    Hassannezhad, Asma
    arXiv.org, Apr 29, 2013
    © ProQuest LLC All rights reserved, Engineering Database, Publicly Available Content Database, ProQuest Engineering Collection, ProQuest Technology Collection, ProQuest SciTech Collection, Materials Science & Engineering Database, ProQuest Central (new), ProQuest Central Korea, SciTech Premium Collection, Technology Collection, ProQuest Central Essentials, ProQuest One Academic, Engineering Collection (ProQuest)
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    Titre: Eigenvalues of the Laplacian and extrinsic geometry
    Auteur: Hassannezhad, Asma
    Contributeur: Hassannezhad, Asma (pacrepositoryorg)
    Sujet: Eigen Values ; Eigenvalues ; Manifolds (Mathematics) ; Invariants ; Upper Bounds ; Spectral Theory ; Differential Geometry
    Description: We extend the results given by Colbois, Dryden and El Soufi on the relationships between the eigenvalues of the Laplacian and an extrinsic invariant called intersection index, in two directions. First, we replace this intersection index by invariants of the same nature which are stable under small perturbations. Second, we consider complex submanifolds of the complex projective space \(\mathbb{C} P^N\) instead of submanifolds of \(\mathbb{R}^N\) and we obtain an eigenvalue upper bound depending only on the dimension of the submanifold which is sharp for the first non-zero eigenvalue.
    Fait partie de: arXiv.org, Apr 29, 2013
    Identifiant: 2331-8422 (E-ISSN)

    • Plusieurs versions

    Eigenvalues of perturbed Laplace operators on compact manifolds

    Hassannezhad, Asma
    arXiv.org, Jan 3, 2013 [Revue évaluée par les pairs]

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    Eigenvalues of the Laplacian and extrinsic geometry

    Hassannezhad, Asma
    Cornell University
    Disponible
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    Titre: Eigenvalues of the Laplacian and extrinsic geometry
    Auteur: Hassannezhad, Asma
    Sujet: Mathematics - Spectral Theory ; Mathematics - Differential Geometry
    Description: We extend the results given by Colbois, Dryden and El Soufi on the relationships between the eigenvalues of the Laplacian and an extrinsic invariant called intersection index, in two directions. First, we replace this intersection index by invariants of the same nature which are stable under small perturbations. Second, we consider complex submanifolds of the complex projective space $\mathbb{C} P^N$ instead of submanifolds of $\mathbb{R}^N$ and we obtain an eigenvalue upper bound depending only on the dimension of the submanifold which is sharp for the first non-zero eigenvalue.
    Identifiant: 1210.7714 (ARXIV ID)

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    A note on Kuttler-Sigillito's inequalities

    Hassannezhad, Asma, Siffert, Anna
    arXiv.org, Sep 28, 2017
    © ProQuest LLC All rights reserved, Engineering Database, Publicly Available Content Database, ProQuest Engineering Collection, ProQuest Technology Collection, ProQuest SciTech Collection, Materials Science & Engineering Database, ProQuest Central (new), ProQuest Central Korea, SciTech Premium Collection, Technology Collection, ProQuest Central Essentials, ProQuest One Academic, Engineering Collection (ProQuest)
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    Titre: A note on Kuttler-Sigillito's inequalities
    Auteur: Hassannezhad, Asma; Siffert, Anna
    Contributeur: Siffert, Anna (pacrepositoryorg)
    Sujet: Brownian Movements ; Eigenvalues ; Riemann Manifold ; Inequalities ; Domains
    Description: We provide several inequalities between eigenvalues of some classical eigenvalue problems on domains with \(C^2\) boundary in complete Riemannian manifolds. A key tool in the proof is the generalized Rellich identity on a Riemannian manifold. Our results in particular extend some inequalities due to Kutller and Sigillito from subsets of \(\mathbb{R}^2\) to the manifold setting.
    Fait partie de: arXiv.org, Sep 28, 2017
    Identifiant: 2331-8422 (E-ISSN)

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    Higher order Cheeger inequalities for Steklov eigenvalues

    Hassannezhad, Asma, Miclo, Laurent
    Cornell University
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    Titre: Higher order Cheeger inequalities for Steklov eigenvalues
    Auteur: Hassannezhad, Asma; Miclo, Laurent
    Sujet: Mathematics - Spectral Theory ; Mathematics - Differential Geometry ; Mathematics - Probability ; 35p15, 58j50, 58j65, 60j25, 60j27
    Description: We prove a lower bound for the $k$-th Steklov eigenvalues in terms of an isoperimetric constant called the $k$-th Cheeger-Steklov constant in three different situations: finite spaces, measurable spaces, and Riemannian manifolds. These lower bounds can be considered as higher order Cheeger type inequalities for the Steklov eigenvalues. In particular it extends the Cheeger type inequality for the first nonzero Steklov eigenvalue previously studied by Escobar in 1997 and by Jammes in 2015 to higher order Steklov eigenvalues. The technique we develop to get this lower bound is based on considering a family of accelerated Markov operators in the finite and mesurable situations and of mass concentration deformations of the Laplace-Beltrami operator in the manifold setting which converges uniformly to the Steklov operator. As an intermediary step in the proof of the higher order Cheeger type inequality, we define the Dirichlet-Steklov connectivity spectrum and show that the Dirichlet connectivity spectra of this family of operators converges to (or bounded by) the Dirichlet-Steklov spectrum uniformly. Moreover, we obtain bounds for the Steklov eigenvalues in terms of its Dirichlet-Steklov connectivity spectrum which is interesting in its own right and is more robust than the higher order Cheeger type inequalities. The Dirichlet-Steklov spectrum is closely related to the Cheeger-Steklov constants. Comment: Correcting few typos and doing some changes on pages 41 and 45
    Identifiant: 1705.08643 (ARXIV ID)

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    Eigenvalue bounds of mixed Steklov problems

    Hassannezhad, Asma, Laptev, Ari
    Cornell University
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    Titre: Eigenvalue bounds of mixed Steklov problems
    Auteur: Hassannezhad, Asma; Laptev, Ari
    Sujet: Mathematics - Spectral Theory ; Mathematical Physics ; Mathematics - Functional Analysis ; 35p15, 35p05, 47f05
    Description: We study bounds on the Riesz means of the mixed Steklov-Neumann and Steklov-Dirichlet eigenvalue problem on a bounded domain $\Omega$ in $\mathbb{R}^n$. The Steklov-Neumann eigenvalue problem is also called the sloshing problem. We obtain two-term asymptotically sharp lower bounds on the Riesz means of the sloshing problem and also provide an asymptotically sharp upper bound for the Riesz means of mixed Steklov-Dirichlet problem. The proof of our results for the sloshing problem uses the average variational principle and monotonicity of sloshing eigenvalues. In the case of Steklov-Dirichlet eigenvalue problem, the proof is based on a well-known bound on the Riesz means of the Dirichlet fractional Laplacian and an inequality between the Dirichlet and Navier fractional Laplacian. The two-term asymptotic results for the Riesz means of mixed Steklov eigenvalue problems are discussed in the appendix which in particular show the asymptotic sharpness of the bounds we obtain. Comment: An appendix by by F. Ferrulli and J. Lagac\'e is added; some changes in the introduction are made
    Identifiant: 1712.00753 (ARXIV ID)

    • Plusieurs versions

    Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds

    Hassannezhad, Asma, Kokarev, Gerasim
    arXiv.org, Jun 26, 2015 [Revue évaluée par les pairs]

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    Eigenvalue bounds of mixed Steklov problems

    Hassannezhad, Asma, Laptev, Ari
    arXiv.org, Sep 6, 2018
    © ProQuest LLC All rights reserved, Engineering Database, Publicly Available Content Database, ProQuest Engineering Collection, ProQuest Technology Collection, ProQuest SciTech Collection, Materials Science & Engineering Database, ProQuest Central (new), ProQuest Central Korea, SciTech Premium Collection, Technology Collection, ProQuest Central Essentials, ProQuest One Academic, Engineering Collection (ProQuest)
    Disponible
    Plus…
    Titre: Eigenvalue bounds of mixed Steklov problems
    Auteur: Hassannezhad, Asma; Laptev, Ari
    Contributeur: Laptev, Ari (pacrepositoryorg)
    Sujet: Eigen Values ; Dirichlet Problem ; Sharpness ; Eigenvalues ; Lower Bounds ; Asymptotic Properties ; Upper Bounds ; Dirichlet Problem ; Spectral Theory ; Functional Analysis ; Mathematical Physics
    Description: We study bounds on the Riesz means of the mixed Steklov-Neumann and Steklov-Dirichlet eigenvalue problem on a bounded domain \(\Omega\) in \(\mathbb{R}^n\). The Steklov-Neumann eigenvalue problem is also called the sloshing problem. We obtain two-term asymptotically sharp lower bounds on the Riesz means of the sloshing problem and also provide an asymptotically sharp upper bound for the Riesz means of mixed Steklov-Dirichlet problem. The proof of our results for the sloshing problem uses the average variational principle and monotonicity of sloshing eigenvalues. In the case of Steklov-Dirichlet eigenvalue problem, the proof is based on a well-known bound on the Riesz means of the Dirichlet fractional Laplacian and an inequality between the Dirichlet and Navier fractional Laplacian. The two-term asymptotic results for the Riesz means of mixed Steklov eigenvalue problems are discussed in the appendix which in particular show the asymptotic sharpness of the bounds we obtain.
    Fait partie de: arXiv.org, Sep 6, 2018
    Identifiant: 2331-8422 (E-ISSN)