Topological properties of eigenfunctions of Riemannian surfaces

Sugata Mondal

doi:10.5802/afst.1610

Sugata Mondal ¹

¹ Indiana University, Rawles Hall, 831 E 3rd Street, Bloomington, Indiana, USA

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 3, pp. 593-618.

Résumé
Abstract

Nous examinons les résultats [37] de B. Sevennec , [28] de J-P. Otal, [29] de J-P. Otal et E. Rosas, [25], [26] de l’auteur et [2], [3] de l’auteur avec ses collaborateurs W. Ballmann et H. Matthiesen. Notre motivation est de donner au lecteur une idée générale de la façon dont, dans ces travaux (relativement) récents, des arguments topologiques ont été utilisés pour prouver des résultats délicats sur la géométrie spectrale des surfaces.

We provide a short survey of the results [37] of B. Sevennec, [28] of J-P. Otal, [29] of J-P. Otal and E. Rosas, [25], [26] of the author and [2], [3] of the author with his collaborators W. Ballmann and H. Matthiesen. The motivation is to give the reader a general idea how, in these (relatively) recent works, topological arguments were used to prove delicate results in the spectral geometry of surfaces.

Publié le : 2019-12-06

DOI : 10.5802/afst.1610

Classification : 58J50, 35P15, 53C99
Mots clés : Laplace operator, multiplicity of an eigenvalue, small eigenvalue

Affiliations des auteurs :

Sugata Mondal ¹

¹ Indiana University, Rawles Hall, 831 E 3rd Street, Bloomington, Indiana, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Topological properties of eigenfunctions of {Riemannian} surfaces},
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Sugata Mondal. Topological properties of eigenfunctions of Riemannian surfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 3, pp. 593-618. doi : 10.5802/afst.1610. https://afst.centre-mersenne.org/articles/10.5802/afst.1610/

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