Communications in Analysis and Geometry

Volume 22 (2014)

Number 3

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

Pages: 387 – 420



Antonio Esteve (IES Alfonso VIII, Cuenca, Spain; Departamento de Análisis Económico y Finanzas, Universidad de Castilla-la Mancha, Spain)

Vicente Palmer (Departament de Matemàtiques, Institute of New Imaging Technologies, Universitat Jaume I, Castellon, Spain)


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 $K_N \leq b \lt 0$.

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