  The electronic band structure of ABC-stacked multilayer graphene is studied
within an effective mass approximation. The electron and hole bands touching at
zero energy support chiral quasiparticles characterized by Berry's phase N pi
for N-layers, generalizing the low-energy band structure of monolayer and
bilayer graphene. We investigate the trigonal-warping deformation of the energy
bands and show that the Lifshitz transition, in which the Fermi circle breaks
up into separate parts at low energy, reflects Berry's phase N pi. It is
particularly prominent in trilayers, N=3, with the Fermi circle breaking into
three parts at a relatively large energy that is related to next-nearest-layer
coupling. For N=3, we study the effects of electrostatic potentials which vary
in the stacking direction, and find that a perpendicular electric field, as
well as opening an energy gap, strongly enhances the trigonal-warping effect.
In magnetic fields, the N=3 Lifshitz transition is manifested as a coalescence
of Landau levels into triply-degenerate levels.
