11 citations · 16 across the 11 of their papers we have counts for
12 papers
Area of convex disks
Gregory R. Chambers, Christopher Croke, Yevgeny Liokumovich +1
This paper considers metric balls in two dimensional Riemannian manifolds when is less than half the convexity radius. We prove that .…
Scattering data versus lens data on surfaces
Christopher B. Croke, Haomin Wen
The scattering data of a Riemannian manifold with boundary record the incoming and outgoing directions of each geodesic passing through. We show that the scattering data of a gener…
Lens rigidity with trapped geodesics in two dimensions
Christopher B. Croke, Pilar Herreros
We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat Möbius strip…
Scattering rigidity with trapped geodesics
Christopher B. Croke
We prove that the flat product metric on is scattering rigid where is the unit ball in and . The scattering data (loosely speaking) of a Riema…
A Zoll counterexample to a geodesic length conjecture
Florent Balacheff, Christopher Croke, Mikhail G. Katz
We construct a counterexample to a conjectured inequality L<2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sph…
A synthetic characterization of the hemisphere
Christopher B. Croke
We show that round hemispheres are the only compact 2 dimensional Riemannian manifolds (with or without boundary) such that almost every pair of complete geodesics intersect once a…