# About hypersurfaces in R^n+1 with bounded 2nd fundamental form

Assume $M^n$ is a compact hypersurface without boundary immersed in $R^{n+1}$, with $A$ its 2nd fundamental form. If the square norm of A is bounded by an abstract constant, i.e. $|A|^2\leq C$ for some constant $C$. Question: Can one pick up a constant $r$ only depends on $C$ and $n$ s.t. for any point $p$ on $M^n$, $M^n$ can be written as a (local) graph in an $n+1$ ball $B_r(p)$. Thanks! Rmk. Notice that $r$ is independent of $M^n$!

• Could you give some context and motivation? This looks like a high-level homework without them (hint: your assumption bounds the derivative of the Gauss map). – Benoît Kloeckner Nov 24 '13 at 9:17