Let M be a Riemannian manifold and \varepsilon > 0. The thin part of M is the subset of points x \in M where the injectivity radius of M at x is less than \varepsilon, usually denoted M_{< \varepsilon}, and the thick part its complement, usually denoted M_{\ge \varepsilon}.
When M is of negative curvature and \varepsilon is smaller than the Margulis constant for \widetilde M the structure of the components of the thin part is very simple.