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Exponential gaps in the length spectrum

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  • 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.

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

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