Rigidity for surfaces of non-positive curvature

Differentiability, rigidity and Godbillon-Vey classes for Anosov flows

“…This function characterizes the isometry class of the metric [8,55]. The class of Zygmund functions most commonly arises in the study of singular integral operators, and defines a natural norm for these kernal operators (cf.…”

“…The first version of this manuscript was circulated in May, 1986, and since that time considerable additional progress has been made in the smooth rigidity theory for Anosov systems (cf. [9,8,11,12,13,14,15,23,26,27,28,33,32,36,37,41,42,55]). …”

“…The estimate (8) implies that for each s > 0, the function f belongs to the s-Sobolev space on R n . As f has compact support, we can then apply the Sobolev lemma to deduce that f is C ∞ .…”

Boundary and Lens Rigidity of Lorentzian Surfaces

“…In doing so he showed that this result follows from the boundary rigidity for domains in Euclidean space, a problem which had already been considered by Gromov [7] and Michel [12]. In another paper Croke [4] gave a very general boundary rigidity result for two dimensional Riemannian manifolds. In [4] Croke introduces the class of strongly geodesically minimizing manifolds, a class of compact manifolds that includes totally convex domains and which seems to be the natural class to consider when dealing with boundary rigidity questions.…”

“…In another paper Croke [4] gave a very general boundary rigidity result for two dimensional Riemannian manifolds. In [4] Croke introduces the class of strongly geodesically minimizing manifolds, a class of compact manifolds that includes totally convex domains and which seems to be the natural class to consider when dealing with boundary rigidity questions. In order to define the analogous notion in the Lorentzian case we make the following definition.…”