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 $K_N\le b<0$

24 pages