  We use the voltage biased tip of a scanning force microscope at a temperature
of 35\,mK to locally induce the fractional quantum Hall state of $\nu=1/3$ in a
split-gate defined constriction. Different tip positions allow us to vary the
potential landscape. From temperature dependence of the conductance plateau at
$G=1/3 \times e^2/h$ we determine the activation energy of this local $\nu=1/3$
state. We find that at a magnetic field of 6\,T the activation energy is
between 153\,$\mu$eV and 194\,$\mu$eV independent of the shape of the confining
potential, but about 50\% lower than for bulk samples.
