TY - JOUR
T1 - Estimations non linéaires pour des hypersurfaces en fonction de leurs formes fondamentales
AU - Malin, Maria
AU - Mardare, Cristinel
PY - 2017/11
Y1 - 2017/11
N2 - 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.
AB - 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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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85032960592&origin=recordpage
U2 - 10.1016/j.crma.2017.10.014
DO - 10.1016/j.crma.2017.10.014
M3 - RGC 21 - Publication in refereed journal
AN - SCOPUS:85032960592
VL - 355
SP - 1196
EP - 1200
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 11
ER -