Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 949–963 | Cite as

The sharp upper bounds for the first positive eigenvalue of the Kohn–Laplacian on compact strictly pseudoconvex hypersurfaces



We give sharp and explicit upper bounds for the first positive eigenvalue \(\lambda _1({\Box _{b}})\) of the Kohn–Laplacian on compact strictly pseudoconvex hypersurfaces in \({\mathbb {C}}^{n+1}\) in terms of their defining functions. As an application, we show that in the family of real ellipsoids, \(\lambda _1({\Box _{b}})\) has a unique maximum value at the CR sphere.


Eigenvalue Kohn–Laplacian 

Mathematics Subject Classification

32V20 32W10 


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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.College of Mathematics and InformaticsFujian Normal UniversityFuzhouChina
  3. 3.Science ProgramTexas A&M University at QatarEducation City, DohaQatar

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