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

摘要

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 KN ≤ b < 0.