The Chern–Osserman inequality for minimal surfaces in a Cartan–Hadamard manifold with strictly negative sectional curvatures

We state and prove a Chern–Osserman-type inequality in terms of the volume growth for minimal surfaces S which have finite total extrinsic curvature and are properly immersed in a Cartan–Hadamard manifold N with sectional curvatures bounded from above by a negative quantity K N ≤ b