Mean curvature and compactification of surfaces in a negatively curved Cartan-Hadamard manifold

Abstract

We state and prove a Chern-Osserman-type inequality in terms of the volume growth for complete surfaces with controlled mean curvature properly immersed in a Cartan-Hadamard manifold N with sectional curvatures bounded from above by a negative quantity K N ≤ b < 0.2000 Mathematics Subject Classification. Primary 53C20, 53C40; Secondary 53C42, 57N05.