3 problems

Let $x$ be a point on a sphere or hyperbolic space, and let $W_x\subset T_x{{\cal M}}$ be the tangent subspace determining the restricted geodesic subspace. Let reference points co…

Let ${{\cal M}}$ be a Riemannian manifold, let $x\in{{\cal M}}$, and let $W_x\subset T_x{{\cal M}}$ be the subspace generated by the first-order tangent vectors of a coalescing con…

Let $X$ be a collection of reference points at infinity in hyperbolic space. Generalize the barycentric subspaces using Busemann functions, and denote the resulting flat and convex…