  We report a study on the crystal growth of the hexagonal manganites
$R$MnO$_3$ ($R$ = Y, Lu, Ho, Er, and Tm) by using an optical floating-zone
method. It was found that high-quality single crystals of $R$ = Y, Lu, and Ho
could be easily grown with essentially the same conditions as those reported in
literature, that is, with an atmosphere of normal pressure Ar and oxygen
mixture and a growth rate of 2--4 mm/h. However, these conditions were not
feasible for growing good crystals of $R$ = Er and Tm. The chemical analysis
indicated that it was due to an off-stoichiometric phenomenon in the formed
single crystals. We used an effective and simple way to resolve this problem by
adjusting the nominal compositions of the polycrystal feed rods to be 1--$2\%$
rare-earth excess. The structures and physical properties were characterized by
X-ray diffraction, magnetic susceptibility, specific heat, resistivity, and
dielectric constant measurements.
