  The inner fission barriers of the even-even uranium isotopes from the proton
to the neutron drip line are studied with the deformed relativistic
Hartree-Bogoliubov theory in continuum. A periodic evolution for the ground
state shapes is shown with the neutron number, i.e., spherical shapes at shell
closures $N=$126, 184, 258, and prolate dominated shapes between them. In
analogy to the shape evolution, the inner fission barriers also exhibit a
periodic behavior: peaks at the shell closures and valleys in the mid-shells.
The triaxial effect to the inner fission barrier is evaluated using the
triaxial relativistic mean field calculations plus a simple BCS method for
pairing. With the triaxial correction included, good consistency in the inner
barrier heights is found with the available empirical data. Besides, the
evolution from the proton to the neutron drip line is in accord with the
results by the multi-dimensionally constrained relativistic mean field theory.
A flat valley in the fission barrier height is predicted around the
neutron-rich nucleus $^{318}$U which may play a role of fission recycling in
the astrophysical $r$-process nucleosynthesis.
