Abstract
We prove that no eigenvalue of the clamped disk can have multiplicity greater than six. Our method of proof is based on a new recursion formula, linear algebra arguments and a transcendence theorem due to Siegel and Shidlovskii.
| Original language | American English |
|---|---|
| Pages (from-to) | 369-383 |
| Number of pages | 15 |
| Journal | Journal of Differential Geometry |
| Volume | 121 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 2022 |
Bibliographical note
Funding Information:from Iosif Polterovich. We are very grateful to Iosif for introducing us to this problem, and explaining to us the beauty and subtle points of several surrounding questions. We would like to thank Enrico Bombieri, who explained to us some ideas of transcendental number theory. This manuscript also benefited from several interesting discussions with Lev Buhovski, Aleksandr Logunov, Eugenia Malinnikova, Guillaume Roy-Fortin, and Mikhail Sodin. This paper is part of the PhD thesis of the first author. The support of the Israel Science Foundation through grants nos. 753/14 and 681/18 is gratefully acknowledged. Part of this work was written while the second author was an invited researcher of the LabEx Mathématiques Hadamard project in Paris-Sud XI and a Chateaubriand France-Israel fellow. The financial supports of the LMH and the French government are gratefully acknowledged.
Funding Information:
We first learned about the clamped plate problem from Iosif Polterovich. We are very grateful to Iosif for introducing us to this problem, and explaining to us the beauty and subtle points of several surrounding questions. We would like to thank Enrico Bombieri, who explained to us some ideas of transcendental number theory. This manuscript also benefited from several interesting discussions with Lev Buhovski, Aleksandr Logunov, Eugenia Malinnikova, Guillaume Roy-Fortin, and Mikhail Sodin. This paper is part of the PhD thesis of the first author. The support of the Israel Science Foundation through grants nos. 753/14 and 681/18 is gratefully acknowledged. Part of this work was written while the second author was an invited researcher of the LabEx Mathématiques Hadamard project in Paris-Sud XI and a Chateaubriand France-Israel fellow. The financial supports of the LMH and the French government are gratefully acknowledged.
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