The Chern–Osserman inequality for minimal surfaces in a Cartan–Hadamard manifold with strictly negative sectional curvatures
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comunitat-uji-handle2:10234/43662
comunitat-uji-handle3:10234/43643
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Title
The Chern–Osserman inequality for minimal surfaces in a Cartan–Hadamard manifold with strictly negative sectional curvaturesDate
2014Publisher
Springer NetherlandsISSN
0004-2080Type
info:eu-repo/semantics/articlePublisher version
http://link.springer.com/article/10.1007/s11512-013-0182-3Version
info:eu-repo/semantics/submittedVersionAbstract
We state and prove a Chern–Osserman-type inequality in terms of the volume growth for minimal surfaces S which have finite total extrinsic curvature and are properly immersed in a Cartan–Hadamard manifold N with ... [+]
We state and prove a Chern–Osserman-type inequality in terms of the volume growth for minimal surfaces S which have finite total extrinsic curvature and are properly immersed in a Cartan–Hadamard manifold N with sectional curvatures bounded from above by a negative quantity K N ≤b<0 and such that they are not too curved (on average) with respect to the hyperbolic space with constant sectional curvature given by the upper bound b. We also prove the same Chern–Osserman-type inequality for minimal surfaces with finite total extrinsic curvature and properly immersed in an asymptotically hyperbolic Cartan–Hadamard manifold N with sectional curvatures bounded from above by a negative quantity K N ≤b<0. [-]
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Arkiv för Matematik, 52, 1, p. 61-92Rights
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info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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