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Large Steklov eigenvalues via homogenisation on manifolds (Q2052221)

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Language	Label	Description	Also known as
English	Large Steklov eigenvalues via homogenisation on manifolds	scientific article

Statements

scholarly article

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Large Steklov eigenvalues via homogenisation on manifolds (English)

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Alexandre Girouard

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Inventiones Mathematicae

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publication date

25 November 2021

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full work available at URL

https://arxiv.org/abs/2004.04044

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zbMATH Keywords

Steklov eigenvalues

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free boundary minimal surfaces

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weighted Laplace eigenvalues

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describes a project that uses

Surface Evolver

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MaRDI profile type

MaRDI publication profile

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Shape optimization by the homogenization method

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Wildly perturbed manifolds: norm resolvent and spectral convergence

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Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)

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Homogenization of harmonic vector fields on Riemannian manifolds with complicated microstructure

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Homogenization of metrics in oscillating manifolds

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The Surface Evolver

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\(L^\infty\) bounds of Steklov eigenfunctions and spectrum stability under domain variation

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Spectra of domains in compact manifolds

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Spectra of manifolds less a small domain

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Large spectral gaps for Steklov eigenvalues under volume constraints and under localized conformal deformations

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On branched minimal immersions of surfaces by first eigenfunctions

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Riemannian Metrics with Large λ 1

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Extremal eigenvalues of the Laplacian in a conformal class of metrics: the `conformal spectrum'

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Spectrum of the Laplacian with weights

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Isoperimetric control of the Steklov spectrum

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Eigenvalues of the Laplacian on a compact manifold with density

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The spectral gap of graphs and Steklov eigenvalues on surfaces

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The Steklov and Laplacian spectra of Riemannian manifolds with boundary

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The Steklov spectrum and coarse discretizations of manifolds with boundary

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Sur la multiplicité de la première valeur propre non nulle du Laplacien. (On the multiplicity of the first nonzero eigenvalue of the Laplacian)

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Homogenization on arbitrary manifolds

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The construction of periodic unfolding operators on some compact Riemannian manifolds

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A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle

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Free boundary minimal surfaces in the unit 3-ball

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Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary

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The first Steklov eigenvalue, conformal geometry, and minimal surfaces

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Minimal surfaces and eigenvalue problems

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Sharp eigenvalue bounds and minimal surfaces in the ball

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Shape optimization for the Steklov problem in higher dimensions

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From Steklov to Neumann via homogenisation

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Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems

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Spectral geometry of the Steklov problem (survey article)

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Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

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A note on Kuttler-Sigillito's inequalities

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Extremal Metric for the First Eigenvalue on a Klein Bottle

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Maximization of Laplace−Beltrami eigenvalues on closed Riemannian surfaces

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Computation of free boundary minimal surfaces <i>via</i> extremal Steklov eigenvalue problems

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Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc

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Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds

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Index of minimal spheres and isoperimetric eigenvalue inequalities

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Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces

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An isoperimetric inequality for Laplace eigenvalues on the sphere

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Variational aspects of Laplace eigenvalues on Riemannian surfaces

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Upper bounds for eigenvalues of conformal metrics

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Inequalities for membrane and Stekloff eigenvalues

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Eigenvalue Optimisation on Flat Tori and Lattice Points in Anisotropically Expanding Domains

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Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues

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Free boundary minimal surfaces in the unit ball : recent advances and open questions

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A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces

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Homogenisation on homogeneous spaces

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Discontinuity of geometric expansions

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A characterization of the critical catenoid

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Berger's isoperimetric problem and minimal immersions of surfaces

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An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane

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Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian

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Weyl-type bounds for Steklov eigenvalues

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Potential and scattering theory on wildly perturbed domains

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Stationary minimal surfaces with boundary on a simplex

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Partial differential equations. I: Basic theory

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Sharp bounds for the first non-zero Stekloff eigenvalues

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Comparison of Steklov eigenvalues on a domain and Laplacian eigenvalues on its boundary in Riemannian manifolds

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Identifiers

zbMATH Open document ID

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10.1007/s00222-021-01058-w

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2052221

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