EXPLICIT RIGIDITY OF ALMOST-UMBILICAL HYPERSURFACES

Abstract : We give an explicit estimate of the distance of a closed, connected, orientable and immersed hypersurface of a space form to a geodesic sphere and show that the spherical closeness can be controlled by a power of an integral norm of the traceless second fundamental form, whenever the latter is sufficiently small. Furthermore we use the inverse mean curvature flow in the hyperbolic space to deduce the best possible order of decay in the class of C ∞-bounded hypersurfaces of the Euclidean space.
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Contributor : Julien Roth <>
Submitted on : Friday, May 22, 2015 - 1:44:29 PM
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Julien Roth, Julian Scheuer. EXPLICIT RIGIDITY OF ALMOST-UMBILICAL HYPERSURFACES. Pacific Journal of Mathematics, 2018, 22 (6), pp.1075-1088. ⟨hal-01154555⟩

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