Area estimates and rigidity of non-compact 𝐻-surfaces in 3-manifolds

Lima, Vanderson

doi:10.1090/proc/14578

Area estimates and rigidity of non-compact $H$-surfaces in 3-manifolds
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Proc. Amer. Math. Soc. 147 (2019), 4499-4512 Request permission

Abstract:

For appropriate values of $H$, we obtain an area estimate for a complete non-compact $H$-surface of finite topology and finite area, embedded in a 3-manifold of negative curvature. Moreover, in the case of equality and under additional assumptions, we prove that a neighborhood of the mean convex side of the surface must be isometric to a hyperbolic Fuchsian manifold. Also, we provide a counterexample showing that, in the case of minimal surfaces, equality in the area estimate does not necessarily imply a local rigidity result for the ambient manifold.

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