A positive mass theorem in the Einstein-Gauss-Bonnet theory

As an interesting application of the Einstein-Gauss-Bonnet theory and our work on the Gauss-Bonnet-Chern mass (Ge, Wang, Wu), we obtain a positive mass theorem for asymptotically flat graphs in ${\mathbb{R}}^{n+1}$ under a condition that $R+\alpha L_2$ is non-negative, where $R$ is the scalar curvature, $\alpha \in \mathbb{R}$ a constant and $L_2$ the second Gauss-Bonnet curvature. A Penrose type inequality is also obtained in the case $\alpha >0$.