Stability analysis of isometric embeddings

2017/12/07 by Norman Zergänge, Zergänge, Norman
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1712.02766

openalex publication_date 2017/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we prove the fact that, for a short time, it is possible to construct a smooth parametrized family of isometric embeddings of an arbitrary smooth parametrized family of Riemannian metrics on a smooth closed manifold into an Euclidean space. In order to prove this statement we work out stability estimates within Matthias Günther's local perturbation method to derive a time-dependent local perturbation method around a free isometric embedding. Iteratively, we use this time-dependent local perturbation method to construct the desired family of isometric embeddings.

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