Estimations non linéaires pour des hypersurfaces en fonction de leurs formes fondamentales

Nonlinear estimates for hypersurfaces in terms of their fundamental forms

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageFrench
Pages (from-to)1196-1200
Number of pages5
Journal / PublicationComptes Rendus Mathematique
Issue number11
Online published7 Nov 2017
Publication statusPublished - Nov 2017
Externally publishedYes



A sufficiently regular hypersurface immersed in the (n+1)-dimensional Euclidean space is determined up to a proper isometry of ℝn+1 by its first and second fundamental forms. As a consequence, a sufficiently regular hypersurface with boundary, whose position and positively-oriented unit normal vectors are given on a non-empty portion of its boundary, is uniquely determined by its first and second fundamental forms. We establish here stronger versions of these uniqueness results by means of inequalities showing that an appropriate distance between two immersions from a domain ω of ℝn into ℝn+1 is bounded by the Lp-norm of the difference between matrix fields defined in terms of the first and second fundamental forms associated with each immersion.

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