  Let V be a compact real analytic surface with isolated singularities embedded
in $R^N$, and assume its smooth part is equipped with a Riemannian metric that
is induced from some analytic Riemannian metric on $R^N$. We prove:
  1. Each point of V has a neighborhood which is quasi-isometric (naturally and
'almost isometrically') to a union of metric cones and horns, glued at their
tips.
  2. A full asymptotic expansion, for any $p\in V$, of the length of
$V\cap\{q:\dist(q,p)=r\}$ as r tends to zero.
  3. A Gauss-Bonnet Theorem, saying that horns do not contribute an extra term,
while cones contribute the leading coefficient in the length expansion of 2.
  4. The $L^2$ Stokes Theorem, self-adjointness and discreteness of the
Laplace-Beltrami operator on the smooth part, and a Gauss-Bonnet Theorem for
the $L^2$ Euler characteristic.
  As a central tool we use resolution of singularities.
