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Topological properties of eigenfunctions of Riemannian surfaces
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 3, pp. 593-618.

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.

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.

Published online:
DOI: 10.5802/afst.1610
Classification: 58J50, 35P15, 53C99
Keywords: Laplace operator, multiplicity of an eigenvalue, small eigenvalue
Sugata Mondal 1

1 Indiana University, Rawles Hall, 831 E 3rd Street, Bloomington, Indiana, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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, Serie 6, Volume 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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