Local marked boundary rigidity under hyperbolic trapping assumptions

TL;DR

This paper proves local marked boundary rigidity for certain manifolds with hyperbolic trapped sets, assuming injectivity of the X-ray transform over symmetric solenoidal 2-tensors, advancing understanding in geometric inverse problems.

Contribution

It establishes local boundary rigidity under hyperbolic trapping assumptions, extending previous results to more general geometric settings.

Findings

Proves local boundary rigidity for manifolds with hyperbolic trapped sets.

Shows injectivity of the X-ray transform implies rigidity.

Extends rigidity results to manifolds with no conjugate points.

Abstract

Under the assumption that the X-ray transform over symmetric solenoidal 2-tensors is injective, we prove that smooth compact connected manifolds with strictly convex boundary, no conjugate points and a hyperbolic trapped set are locally marked boundary rigid.