Persistence barcodes and Laplace eigenfunctions on surfaces

TL;DR

This paper investigates the properties of persistence barcodes derived from Laplace-Beltrami eigenfunctions on surfaces, providing restrictions and applications to approximation problems.

Contribution

It introduces new restrictions on persistence barcodes of Laplace eigenfunctions and explores their applications in uniform approximation on surfaces.

Findings

Restrictions on persistence barcodes for eigenfunctions

Applications to uniform approximation by eigenfunctions

Insights into the structure of eigenfunctions on surfaces

Abstract

We obtain restrictions on the persistence barcodes of Laplace-Beltrami eigenfunctions and their linear combinations on compact surfaces with Riemannian metrics. Some applications to uniform approximation by linear combinations of Laplace eigenfunctions are also discussed.