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

Antonio Esteve; Vicente Palmer

arxiv: 1206.6748 · v1 · pith:2PZBMVH2new · submitted 2012-06-28 · 🧮 math.DG

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

Antonio Esteve , Vicente Palmer This is my paper

classification 🧮 math.DG

keywords cartan-hadamardcurvaturemanifoldmeansurfacesaboveboundedchern-osserman-type

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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 $K_{N}\leq b<0$

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

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