Let we assume $H$ is mean curvature of a compact surface in $E^3$ and $g$ is its genus.  
(1)When $g$ is arbitrary, we have $\int_{S^{2}}H^{2}dV=4\pi$ and $\int_{\Sigma}H^{2}dV\geq4\pi$.   
(2)When $g=1$, we have $\int_{T^{2}}H^{2}dV\geq2\pi^{2}$ and $\int_{\Sigma}H^{2}dV\geq2\pi^{2}$.  
(3)I want to ask can these theorems be generalized to a compact surface whose $g>1$ in $E^3$? And the statement below is right or not?  
0.0When $g(\Sigma_{1})>g(\Sigma_{2})$, then we have $\int_{\Sigma_{1}}H^{2}dV\geq\int_{\Sigma_{2}}H^{2}dV$.