A geometry where everything is better than nice

2016/03/21 by Larry Bates, Bates, Larry, Peter Gibson +1
Mathematics · #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C25

paper · pdf · doi:10.48550/arxiv.1603.06622

6 pages, to appear in Proceedings of the AMS

arxiv created 2016/03/21 · arxiv updated 2016/03/23

Abstract

We present a riemannian structure on the disk that has a remarkably rich structure. Geodesics are hypocycloids and the (negative of the) laplacian has integer spectrum with multiplicity the Dirichlet divisor function. Eigenfunctions of the laplacian are orthogonal polynomials naturally suited to the analysis of acoustic scattering in layered media.

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