Stability analysis of isometric embeddings
Differential Geometry
2017-12-08 v1 Analysis of PDEs
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 G\"unther'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.
Cite
@article{arxiv.1712.02766,
title = {Stability analysis of isometric embeddings},
author = {Norman Zergänge},
journal= {arXiv preprint arXiv:1712.02766},
year = {2017}
}