Surfaces not quasi-isometric to leaves of foliations of compact 3-manifolds (Q2771415)

The main theorem of the paper is the following: Any connected non-compact 2-manifold \(L\) admits a \(C^{\infty}\) complete Riemannian metric \(g\) with bounded geometry such that it is not quasi-isometric to any leaf of a codimension one \(C^1\) foliation on any compact 3-manifold. Furthermore, \(g\) can be chosen such that no end of \(L\) is quasi-isometric to an end of a leaf of such a foliation, and also to have any growth type compatible with bounded geometry. In fact, for each open surface and compatible growth type, there are uncountably many quasi-isometry equivalence classes of such metrics \(g\).NEWLINENEWLINEFor the entire collection see [Zbl 0953.00036].