Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary

Abstract The sphericalization procedure converts a Euclidean space into compact sphere. In this note we propose variant of for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations that depend only on the distance to boundary space. This deformation is bi-Lipschitz original domain near its boundary, but transforms bounded domain. We will show if uniform with respect completion, then transformed also