Noncommutative Laplacian and numerical approximation of Laplace-Beltrami spectrum of compact Riemann surfaces

2025/10/10 by Damien Tageddine, Tageddine, Damien, Jean‐Christophe Nave +1
Mathematics · #Spectral Theory in Mathematical Physics #Algebraic and Geometric Analysis #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2510.09909

Abstract

We derive a numerical approximation of the Laplace-Beltrami operator on compact surfaces embedded in ℝ³ with an axial symmetry. To do so we use a noncommutative Laplace operator defined on the space of finite dimensional hermitian matrices. This operator is derived from a foliation of the surface obtained under an S¹-action on the surface. We present numerical results in the case of the sphere and a generic ellipsoid.

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