Marked Length Spectrum Rigidity for Surface Amalgams

Yandi Wu

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arXiv · 2310.09968

Marked Length Spectrum Rigidity for Surface Amalgams

Yandi Wu

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Abstract

In this paper, we show that simple, thick negatively curved two-dimensional P-manifolds, a large class of surface amalgams, are marked length spectrum rigid. That is, if two piecewise negatively curved Riemannian metrics (satisfying certain smoothness conditions) on a simple, thick two-dimensional P-manifold assign the same lengths to all closed geodesics, then they differ by an isometry up to isotopy. Our main theorem is a natural generalization of Croke and Otal's celebrated results about marked length spectrum rigidity of negatively curved surfaces.

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Yandi Wu. 2023-10-15. Marked Length Spectrum Rigidity for Surface Amalgams. https://arxiv.org/abs/2310.09968

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