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ON COMPACT EMBBEDED WEINGARTEN HYPERSURFACES IN WARPED PRODUCTS

Abstract : We show that compact embedded starshaped r-convex hypersurfaces of certain warped products satisfying Hr = aH + b with a 0, b > 0, where H and Hr are respectively the mean curvature and r-th mean curvature is a slice. In the case of space forms, we show that without the assumption of starshapedness, such Weingarten hypersurfaces are geodesic spheres. Finally, we prove that, in the case of space forms, if Hr − aH − b is close to 0 then the hypersurface is close to geodesic sphere for the Hausdorff distance. We also prove an anisotropic version of this stability result in the Euclidean space.
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Preprints, Working Papers, ...
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https://hal-upec-upem.archives-ouvertes.fr/hal-03682396
Contributor : Julien Roth Connect in order to contact the contributor
Submitted on : Tuesday, May 31, 2022 - 9:26:36 AM
Last modification on : Monday, August 1, 2022 - 10:40:58 AM

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  • HAL Id : hal-03682396, version 1

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Julien Roth, Abhitosh Upadhyay. ON COMPACT EMBBEDED WEINGARTEN HYPERSURFACES IN WARPED PRODUCTS. 2022. ⟨hal-03682396⟩

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