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.
Mots-clés : Laplace operator, multiplicity of an eigenvalue, small eigenvalue
Sugata Mondal 1

@article{AFST_2019_6_28_3_593_0, author = {Sugata Mondal}, title = {Topological properties of eigenfunctions of {Riemannian} surfaces}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {593--618}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 28}, number = {3}, year = {2019}, doi = {10.5802/afst.1610}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1610/} }
TY - JOUR AU - Sugata Mondal TI - Topological properties of eigenfunctions of Riemannian surfaces JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2019 SP - 593 EP - 618 VL - 28 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1610/ DO - 10.5802/afst.1610 LA - en ID - AFST_2019_6_28_3_593_0 ER -
%0 Journal Article %A Sugata Mondal %T Topological properties of eigenfunctions of Riemannian surfaces %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2019 %P 593-618 %V 28 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1610/ %R 10.5802/afst.1610 %G en %F AFST_2019_6_28_3_593_0
Sugata Mondal. Topological properties of eigenfunctions of Riemannian surfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume spécial en l’honneur de Jean-Pierre OTAL “Low dimensional topology, hyperbolic manifolds and spectral geometry”, 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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