A curvature inequality is established for contractive commuting tuples of operators in the Cowen–Douglas class of rank defined on some bounded domain in . Properties of the extremal operators (that is, the operators which achieve equality) are investigated. Specifically, a substantial part of a well-known question due to R. G. Douglas involving these extremal operators, in the case of the unit disc, is answered.
"Curvature inequalities and extremal operators." Illinois J. Math. 63 (2) 193 - 217, August 2019. https://doi.org/10.1215/00192082-7768711