  The Christoffel problem is equivalent to the existence of convex solutions to
the Laplace equation on the unit sphere $S^n$. Necessary and sufficient
conditions have been found by Firey and Berg, using the Green function of the
Laplacian on the sphere. Expressing the Christoffel problem as the Laplace
equation on the entire space $R^{n+1}$, we observe that the second derivatives
of the solution can be given by the fundamental solutions of the Laplace
equations. Therefore we find new and simpler necessary and sufficient
conditions for the solvability of the Christoffel problem. We also study the
$L_p$ extension of the Christoffel problem and provide sufficient conditions
for the problem, for the case $p\geq 2$.
