  Ultra-thin 3D topological insulators provide a stage to study the surface
physics of such materials by minimizing the bulk contribution. Further, the
experimentally verified snowflake like structure of the Fermi surface leads to
a hexagonal warping term, and this discourse examines it as a perturbation in
the presence of a magnetic field. We find that there are corrections to both
energy dispersion and eigenstates which in turn alter the density of states in
the presence of a magnetic field. Both the quantum capacitance and the Hall
coefficient are evaluated analytically and it is shown here that we recover
their established forms along with small corrections which preserve the object
of treating hexagonal warping perturbatively. In our approach, the established
Hall conductivity expression develops several minute correction terms and thus
its behavior remains largely unaffected due to warping. The zero-temperature
quantum capacitance exhibits SdH oscillations with reduced frequencies, with a
lowered average capacitance with increased warping of the Fermi surface, while
maintaining the usual amplitudes.
