  We present high-precision experimental and numerical studies of the Nusselt
number $Nu$ as functions of the Rayleigh number $Ra$ in geostrophic rotating
convection with domain aspect ratio ${\Gamma}$ varying from 0.4 to 3.8 and the
Ekman number Ek from $2.0{\times}10^{-7}$ to $2.7{\times}10^{-5}$. The
heat-transport data $Nu(Ra)$ reveal a gradual transition from
buoyancy-dominated to geostrophic convection at large $Ek$, whereas the
transition becomes sharp with decreasing $Ek$. We determine the power-law
scaling of $Nu{\sim}Ra^{\gamma}$, and show that the boundary flows give rise to
pronounced enhancement of $Nu$ in a broad range of the geostrophic regime,
leading to reduction of the scaling exponent ${\gamma}$ in small ${\Gamma}$
cells. The present work provides new insight into the heat-transport scaling in
geostrophic convection and may explain the discrepancies observed in previous
studies.
