Global eigenfamilies on closed manifolds

2024/01/31 by Riedler, Oskar, Siffert, Anna · 1 citation
#35J05 #53C43 #58E40 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.17750

Abstract

We study globally defined (λ,μ)-eigenfamilies on closed Riemannian manifolds. Among others, we provide (non-)existence results for such eigenfamilies, examine their topological properties and classify (λ,μ)-eigenfamilies on flat tori. It is further shown that for f=f₁+i f₂ being an eigenfunction decomposed into its real and its imaginary part, the powers \f₁^a f₂^b| a,b∈\mathbb N\ satisfy highly rigid orthogonality relations in L²(M). In establishing these orthogonality relations one is led to combinatorial identities involving determinants of products of binomials, which we view as being of independent interest.

Cited by

• Complete Minimal Submanifolds of the Non-Compact Duals to the Classical Compact Lie Groups

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