Bounds on Multiplicities of Laplace-Beltrami Operator Eigenvalues on the Real Projective Plane

TL;DR

This paper improves upper bounds on the multiplicities of Laplace-Beltrami eigenvalues on the real projective plane, especially for even-indexed eigenvalues, and extends results to eigenvalues with boundary conditions.

Contribution

It provides new upper bounds for eigenvalue multiplicities on the real projective plane and for eigenvalues with boundary conditions such as Dirichlet, Neumann, and Steklov.

Findings

Improved bounds for eigenvalue multiplicities on the real projective plane.

Derived bounds for Dirichlet, Neumann, and Steklov eigenvalues with holes.

Enhanced understanding of eigenvalue multiplicities in geometric analysis.

Abstract

The known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenvalues on the real projective plane are improved for the eigenvalues with even indexes. Upper bounds for Dirichlet, Neumann and Steklov eigenvalues on the real projective plane with holes are also provided.