Persistence barcodes and Laplace eigenfunctions on surfaces

2017/11/20 by Polterovich, Iosif, Polterovich, Leonid, Stojisavljević, Vukašin · 1 citation
#55U99 #58J50 #Algebraic Topology (math.AT) #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1711.07577

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.

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• Coarse nodal counts on sub-Riemannian manifolds

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