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Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere

  • * Corresponding author: Yoshitsugu Kabeya

    * Corresponding author: Yoshitsugu Kabeya

Dedicated to Professor Wei-Ming Ni on the occasion of his seventieth birthday

The author is supported in part by JSPS KAKENHI Grant Numbers 15K04965 and 15H03631

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  • We consider the eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a spherical domain. Especially, we investigate the case when the domain is a large zonal one and letting the zone larger so that the zone covers the whole sphere as a limit. We discuss the behavior of eigenvalues according to the rate of expansion of the zone.

    Mathematics Subject Classification: Primary: 35J15, 35P15; Secondary: 35J25, 33C55.


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