2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170854Estimates of the Kobayashi metric in the normal direction are used to study the mapping problem in several complex variables.13 pages; to appear in the special issue of Complex Variables and Elliptic Equations on holomorphic mappings edited by Steven Krantz and John Erik FornaessComplex Variables32F45; 32H40The Kobayashi metric in the normal direction and the mapping problemtext