  In this paper we show boundary monotonicity formulae for rectifiable
varifolds having a $C^{1,\alpha}$ "boundary". In particular, we show that the
area ratios of balls centered at this "boundary'' satisfy a nice monotonicity
formula, similar to that for interior balls (proved in Allard's paper "On the
first variation of a varifold''). This extends the boundary monotonicity
formulae of Allard (see "On the first variation of a varifold- boundary
behavior''), which require that the boundary is $C^{1,1}$. As a corollary,
Allard's boundary regularity results extend to this case and provide a
regularity result for rectifiable varifolds with a $C^{1,\alpha}$ ``boundary''.
