In the paper we prove Nash's theorem, stating that any smooth short embedding from a manifold to R^n can be approximated by C^1 isometric embeddings. As a corollary, we show that any Riemannian manifold can be embedded in Euclidean space.

In the paper we prove Nash's theorem, stating that any smooth short embedding from a manifold to R^n can be approximated by C^1 isometric embeddings. As a corollary, we show that any Riemannian manifold can be embedded in Euclidean space.

C^1 isometric embeddings

MORESCALCHI, ALESSANDRO
2022/2023

Abstract

In the paper we prove Nash's theorem, stating that any smooth short embedding from a manifold to R^n can be approximated by C^1 isometric embeddings. As a corollary, we show that any Riemannian manifold can be embedded in Euclidean space.
2022
C^1 isometric embeddings
In the paper we prove Nash's theorem, stating that any smooth short embedding from a manifold to R^n can be approximated by C^1 isometric embeddings. As a corollary, we show that any Riemannian manifold can be embedded in Euclidean space.
Nash-Kuiper theorem
Isometric embedding
Short map
DifferentialGeometry
VITTONE, DAVIDE
Lauree triennali
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/46804