  We study the dynamics of a one-component liquid constrained on a spherical
substrate, a 2-sphere, and investigate how the mode-coupling theory (MCT) can
describe the new features brought by the presence of curvature. To this end we
have derived the MCT equations in a spherical geometry. We find that, as seen
from the MCT, the slow dynamics of liquids in curved space at low temperature
does not qualitatively differ from that of glass-forming liquids in Euclidean
space. The MCT predicts the right trend for the evolution of the relaxation
slowdown with curvature but is dramatically off at a quantitative level.
