[Sur la reconstruction et la continuité d'une sous-variété à bord en dimensions supérieures.]
Let ω be a connected and simply connected open subset of endowed with a Riemannian metric. Under a smoothness assumption on the boundary of ω, we first establish the existence and uniqueness up to isometries of an isometric immersion of ω into the Euclidean space , ‘up to the boundary’ of ω. When ω is bounded, we also show that the mapping that associates with the prescribed geometrical data the reconstructed submanifold is locally Lipschitz-continuous with respect to the topology of the Banach spaces .
Soit ω un ouvert connexe et simplement connexe de , muni d'une métrique riemannienne. Sous une certaine hypothèse de régularité sur la frontière de ω, on établit d'abord l'existence et l'unicité aux isométries près d'une immersion isométrique de ω dans l'espace euclidien , « jusqu'au bord » de ω. Lorsque ω est borné, on montre aussi que l'application qui associe aux données géométriques prescrites la sous-variété ainsi reconstruite est localement lipschitzienne pour les topologies usuelles des espaces de Banach .
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Szopos, Marcela 1
@article{CRMATH_2004__339_4_265_0,
author = {Szopos, Marcela},
title = {On the recovery and continuity of a submanifold with boundary in higher dimensions},
journal = {Comptes Rendus. Math\'ematique},
pages = {265--270},
year = {2004},
publisher = {Elsevier},
volume = {339},
number = {4},
doi = {10.1016/j.crma.2004.05.022},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2004.05.022/}
}
TY - JOUR AU - Szopos, Marcela TI - On the recovery and continuity of a submanifold with boundary in higher dimensions JO - Comptes Rendus. Mathématique PY - 2004 SP - 265 EP - 270 VL - 339 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2004.05.022/ DO - 10.1016/j.crma.2004.05.022 LA - en ID - CRMATH_2004__339_4_265_0 ER -
%0 Journal Article %A Szopos, Marcela %T On the recovery and continuity of a submanifold with boundary in higher dimensions %J Comptes Rendus. Mathématique %D 2004 %P 265-270 %V 339 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2004.05.022/ %R 10.1016/j.crma.2004.05.022 %G en %F CRMATH_2004__339_4_265_0
Szopos, Marcela. On the recovery and continuity of a submanifold with boundary in higher dimensions. Comptes Rendus. Mathématique, Tome 339 (2004) no. 4, pp. 265-270. doi: 10.1016/j.crma.2004.05.022
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