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Orthospectrum and simple orthospectrum rigidity: finiteness and genericity

2024/12/19 by Nolwenn Le Quellec, Quellec, Nolwenn Le
Business, Management and Accounting · #FOS: Mathematics #Geometric Topology (math.GT) #Optics and Image Analysis

paper · pdf · doi:10.48550/arxiv.2412.15034

openalex publication_date 2024/12/19 · openalex created_date 2024/12/21 · openalex updated_date 2026/07/28

Abstract

We study the orthospectrum and the simple orthospectrum of compact hyperbolic surfaces with geodesic boundary. We show that there are finitely many hyperbolic surfaces sharing the same simple orthospectrum and finitely many hyperbolic surfaces sharing the same orthospectrum. Then, we show that generic surfaces are determined by their orthospectrum and by their simple orthospectrum. We conclude with the example of the one-holed torus which is determined by its simple orthospectrum.

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