Title: On Chern number inequality in dimension 3,
Abstract: We prove that if $X---> X^+$ is a threefold terminal flip, then
$c_1(X).c_2(X)\leq c_1(X^+).c_2(X^+)$ where $c_1(X)$ and $c_2(X)$ denote the
Chern classes. This gives the affirmative answer to a Question by Xie
\cite{Xie2}. We obtain the similar but weaker result in the case of divisorial
contraction to curves.