Exponential gaps in the length spectrum

Emmanuel Schenck

doi:10.3934/jmd.2020007

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2020, Volume 16: 207-223. Doi: 10.3934/jmd.2020007

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Exponential gaps in the length spectrum

Emmanuel Schenck

Laboratoire d'analyse, géométrie et applications, Université Paris 13, CNRS UMR 7539, 99 avenue Jean Baptiste Clément, 93430 Villetaneuse, France

Received: November 10, 2018

Revised: March 29, 2020

Published: June 2020

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Abstract

We present a separation property for the gaps in the length spectrum of a compact Riemannian manifold with negative curvature. In arbitrary small neighborhoods of the metric for some suitable topology, we show that there are negatively curved metrics with a length spectrum exponentially separated from below. This property was previously known to be false generically.

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Mathematics Subject Classification: Primary: 37C25, 53C22; Secondary: 37C20, 37D20, 53D25.

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