  In this article, we study the Lipschitz Geometry at infinity of complex
analytic sets and we obtain results on algebraicity of analytic sets and on
Bernstein's problem. Moser's Bernstein Theorem says that a minimal hypersurface
which is a graph of an entire Lipschitz function must be a hyperplane. H. B.
Lawson, Jr. and R. Osserman presented examples showing that an analogous result
for arbitrary codimension is not true. In this article, we prove a complex
non-parametric version of Moser's Bernstein Theorem. More precisely, we prove
that any entire complex analytic set in $\mathbb{C}^n$ which is Lipschitz
regular at infinity must be an affine linear subspace of $\mathbb{C}^n$. In
particular, a complex analytic set which is a graph of an entire Lipschitz
function must be affine linear subspace. That result comes as a consequence of
the following characterization of algebraic sets, which is also proved here: if
$X$ and $Y$ are entire complex analytic sets which are bi-Lipschitz
homeomorphic at infinity then $X$ is a complex algebraic set if and only if $Y$
is a complex algebraic set too. Thus, an entire complex analytic set is a
complex algebraic set if and only if it is bi-Lipschitz homeomorphic at
infinity to a complex algebraic set. No restrictions on the singular set,
dimension nor codimension are required in the results proved here.
