  Let $G: S^{4n-1} \rightarrow S^{2n}$ be a map with nonzero Hopf Invariant.
Using the generalized Hopf invariant introduced by Haj\l{}asz, Schikorra and
Tyson, we show that any null-homotopy $F: B^{4n} \rightarrow B^{2n+1}$ of $G$
with small $(2n+1)$-dilation must have large $(2n)$-dilation. Conversely, we
show that these results are sharp by constructing smooth null-homotopies with
arbitrarily small $(2n+1)$-dilation.
