TY - JOUR
T1 - Smoothing and inversion of differential operators
AU - Gromov, M. L.
PY - 1972/4/30
Y1 - 1972/4/30
N2 - Nash’s implicit function theorem is generalized. The analytical results are applied to the problem of isometric immersion; in particular, the realizability in Euclidean space of real-analytic Riemannian manifolds is demonstrated. Moreover, theorems about the existence, approximation, extension and transversality of isometric immersion and related maps are stated; deformations and questions about unique definability are also investigated. In addition to the implicit function theorem, the theory of topological sheaves is used.
AB - Nash’s implicit function theorem is generalized. The analytical results are applied to the problem of isometric immersion; in particular, the realizability in Euclidean space of real-analytic Riemannian manifolds is demonstrated. Moreover, theorems about the existence, approximation, extension and transversality of isometric immersion and related maps are stated; deformations and questions about unique definability are also investigated. In addition to the implicit function theorem, the theory of topological sheaves is used.
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U2 - 10.1070/SM1972v017n03ABEH001514
DO - 10.1070/SM1972v017n03ABEH001514
M3 - Article
AN - SCOPUS:18144391770
SN - 0025-5734
VL - 17
SP - 381
EP - 435
JO - Mathematics of the USSR - Sbornik
JF - Mathematics of the USSR - Sbornik
IS - 3
ER -