  B\"or\"oczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski
inequality which is stronger than the classical Brunn-Minkowski inequality for
two origin-symmetric convex bodies in the plane. This paper establishes the
log-Brunn-Minkowski, log-Minkowski, $L_p$-Minkowski and $L_p$-Brunn-Minkowski
inequalities for two convex bodies in $\mathbb{R}^3$.
