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The class of Euclidean spatial conformal mappings is generated by reflections across planes and inversions about spheres.  We briefly recall the concept of Euclidean inversion about a sphere, and then define a notion of inversion valid in the general metric space setting and establish several basic facts concerning these.  For example, they are quasimoebius homeomorphisms and quasihyperbolically bilipschitz.  Just as in the Euclidean setting, sphericalization can be realized as a special case of inversion. Certain important geometric properties are preserved under inversion. For example, both inversion and sphericalization preserve the class of uniform subspaces.

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We introduce a notion called annular quasiconvexity and demonstrate that a space is quasiconvex and annular quasiconvex if and only if its inversions and its sphericalizations also enjoy these properties. Moreover, in the presence of an annular quasiconvex ambient space, we obtain improved quantitative information describing how uniformity constants change.
Examples of metric spaces that are quasiconvex and annular quasiconvex include Banach spaces and upper regular Loewner spaces; the latter includes Carnot groups and certain Riemannian manifolds with non-negative Ricci curvature.
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