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Explicit Rigidity of Almost-umbilical Hypersurfaces by Roth, Julien; Scheuer, Julian is a scholarly article available to read on EtoBox.

What is Explicit Rigidity of Almost-umbilical Hypersurfaces about?

We give an explicit estimate of the distance of a closed, connected, oriented 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 $C^{\infty}$-bounded hypersurfaces of the Euclidean space.

Author

Roth, Julien; Scheuer, Julian

Published

2015

Language

EN