  We $\delta$-approximate strictly short (e.g. constant) maps between Riemannin
manifolds $f_0:X^m\to Y^N$ for $N>>m^2/2$ by $C^\infty$-smooth isometric
immersions $f_\delta:X^m\to Y^N$ with curvatures $curv(f_\delta) < \frac {\sqrt
3}{\delta}$, for $\delta\to 0$
