Smoothing and inversion of differential operators

Mikhael Gromov

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)381-435
Number of pages55
JournalMathematics of the USSR - Sbornik
Volume17
Issue number3
DOIs
StatePublished - Apr 30 1972

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Isometric Immersion
Implicit Function Theorem
Differential operator
Smoothing
Inversion
Transversality
Definability
Realizability
Sheaves
Riemannian Manifold
Euclidean space
Approximation
Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Smoothing and inversion of differential operators. / Gromov, Mikhael.

In: Mathematics of the USSR - Sbornik, Vol. 17, No. 3, 30.04.1972, p. 381-435.

Research output: Contribution to journalArticle

Gromov, Mikhael. / Smoothing and inversion of differential operators. In: Mathematics of the USSR - Sbornik. 1972 ; Vol. 17, No. 3. pp. 381-435.
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