English

Arc criterion of normal embedding

Metric Geometry 2017-10-06 v1

Abstract

We present a criterion of local Normal Embedding of a semialgebraic (or definable in an o-minimal structure) contained in RnR^n in terms orders of contact of arcs. Namely, we prove that a semialgebraic set is normally embedded at a point x if and only if for any pair of arcs, coming to this point the inner order of contact is equal to the outer order of contact.

Keywords

Cite

@article{arxiv.1710.01811,
  title  = {Arc criterion of normal embedding},
  author = {Lev Birbrair and Rodrigo Mendes},
  journal= {arXiv preprint arXiv:1710.01811},
  year   = {2017}
}

Comments

4 pages

R2 v1 2026-06-22T22:04:05.315Z