BOUNDED MULTIPLICITY FOR EIGENVALUES OF A CIRCULAR VIBRATING CLAMPED PLATE

Yuri Lvovsky, Dan Mangoubi

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)369-383
Number of pages15
JournalJournal of Differential Geometry
Volume121
Issue number2
DOIs
StatePublished - 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.

Publisher Copyright:
© 2022 International Press of Boston, Inc.. All rights reserved.

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