Communications in Analysis and Geometry
Volume 22 (2014)
Mean curvature and compactification of surfaces in a negatively curved Cartan-Hadamard manifold
Pages: 387 – 420
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 $K_N \leq b \lt 0$.