  Changes of external parameters in proximity of critical point can increase
thermal fluctuations of tubular lipid membrane (TLM) and result in variation of
the membrane shape. The phase transitions in the system are shown to be
controlled by a single effective parameter, which depends on the pressure
difference between inner and outer regions of membrane and the applied
stretching force. We determine an interval of the parameter values
corresponding to the stability region of the cylindrical shape of TLM and
investigate the behavior of the system in the vicinity of critical
instabilities, where the cylindrical shape of membrane becomes unstable with
respect to thermal fluctuations. The applied boundary conditions strongly
influence the behavior of TLM. For example, small negative effective parameter
corresponds to chiral shape of TLM only in the case of periodic boundary
conditions. We also discuss other three types of phase transitions emerging in
the system.
