Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces

Arias-Marco, Teresa; Dryden, Emily B.; Gordon, Carolyn S.; Hassannezhad, Asma; Ray, Allie; Stanhope, Elizabeth

doi:10.1016/j.jmaa.2024.128088

Journal of Mathematical Analysis and Applications

2024

DOI: 10.1016/j.jmaa.2024.128088

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Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces

Teresa Arias-Marco,

Emily B. Dryden,

Carolyn S. Gordon

et al.

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Some recent developments on the Steklov eigenvalue problem

Colbois,

Girouard,

Gordon

et al. 2023

Rev Mat Complut

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The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of interest in the past few decades. This article is a tour of some of the recent developments linking the Steklov eigenvalues and eigenfunctions of compact Riemannian manifolds to the geometry of the manifolds. Topics include isoperimetric-type upper and lower bounds on Steklov eigenvalues (first in the case of surfaces and then in higher dimensions), stability and instability of eigenvalues under deformations of the Riemannian metric, optimisation of eigenvalues and connections to free boundary minimal surfaces in balls, inverse problems and isospectrality, discretisation, and the geometry of eigenfunctions. We begin with background material and motivating examples for readers that are new to the subject. Throughout the tour, we frequently compare and contrast the behavior of the Steklov spectrum with that of the Laplace spectrum. We include many open problems in this rapidly expanding area.

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Some recent developments on the Steklov eigenvalue problem

Colbois,

Girouard,

Gordon

et al. 2023

Rev Mat Complut

View full text Add to dashboard Cite

show abstract

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Applications of possibly hidden symmetry to Steklov and mixed Steklov problems on surfaces

Cited by 1 publication

References 34 publications

Some recent developments on the Steklov eigenvalue problem

Some recent developments on the Steklov eigenvalue problem

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