  The boundary effects on the Bose-Einstein condensation of a Bose gas with a
nonvanishing chemical potential on an ultra-static space-time are studied. High
temperature regime, which is the relevant regime for the relativistic gas, is
studied through the heat kernel expansion for both Dirichlet and Neumann
boundary conditions. The high temperature expansion in the presence of a
chemical potential is generated via the Mellin transform methods as applied to
the harmonic sums representing the free energy and the depletion coefficient.
The effects of boundary conditions on the relation between depletion
coefficient and temperature are analyzed. The analysis is done for both charged
and neutral bosons.
