On the isometric version of Whitney's strong embedding theorem

On the isometric version of Whitney's strong embedding theorem

We prove a version of Whitney's strong embedding theorem for isometric embeddings within the general setting of the Nash-Kuiper h-principle. More precisely, we show that any n-dimensional smooth compact manifold admits infinitely many global isometric embeddings into 2n-dimensional Euclidean sp...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2025-01, Vol.460, p.110040, Article 110040
Hauptverfasser: Cao, Wentao, Székelyhidi, László
Format: Artikel
Sprache:eng
Schlagworte:
Absorbing higher order error
Convex integration
Corrugation
Isometric embedding
Nash-Kuiper theorem
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Zusammenfassung:We prove a version of Whitney's strong embedding theorem for isometric embeddings within the general setting of the Nash-Kuiper h-principle. More precisely, we show that any n-dimensional smooth compact manifold admits infinitely many global isometric embeddings into 2n-dimensional Euclidean space, of Hölder class C1,θ with θ
ISSN:0001-8708
DOI:10.1016/j.aim.2024.110040