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- W2519322855 abstract "We study complete finite topology immersed surfaces $Sigma$ in complete Riemannian $3$-manifolds $N$ with sectional curvature $K_Nleq -a^2leq 0$, such that the absolute mean curvature function of $Sigma$ is bounded from above by $a$ and its injectivity radius function is not bounded away from zero on each of its annular end representatives. We prove that such a surface $Sigma$ must be proper in $N$ and its total curvature must be equal to $2pi chi(Sigma)$. If $N$ is a hyperbolic $3$-manifold of finite volume and $Sigma$ is a properly immersed surface of finite topology with nonnegative constant mean curvature less than 1, then we prove that each end of $Sigma$ is asymptotic (with finite positive multiplicity) to a totally umbilic annulus, properly embedded in $N$." @default.
- W2519322855 created "2016-09-23" @default.
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- W2519322855 date "2016-03-07" @default.
- W2519322855 modified "2023-09-27" @default.
- W2519322855 title "Properly immersed surfaces in hyperbolic 3-manifolds" @default.
- W2519322855 hasPublicationYear "2016" @default.
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