Boundary rigidity of negatively-curved asymptotically hyperbolic surfaces

TL;DR

This paper proves that negatively-curved asymptotically hyperbolic surfaces are uniquely determined by boundary distance data, extending rigidity results to a broader class of geometric structures using a renormalized distance concept.

Contribution

It establishes boundary distance rigidity for asymptotically hyperbolic surfaces, generalizing prior results to include surfaces with negative curvature and asymptotic hyperbolicity.

Findings

Boundary distance rigidity holds for negatively-curved asymptotically hyperbolic surfaces.

A renormalized boundary distance is used to define distances at infinity.

The result extends classical rigidity theorems to new geometric settings.

Abstract

In the spirit of Otal and Croke, we prove that a negatively-curved asymptotically hyperbolic surface is boundary distance rigid, where the distance between two points on the boundary at infinity is defined by a renormalized quantity.