Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On link of Lipschitz normally embedded sets   A path connected subanalytic subset in $\mathbb{R}^n$ is naturally equipped
with two metrics: the inner and the outer metrics. We say that a subset is
Lipschitz normally embedded (LNE) if these two metrics are equivalent. In this
article, we give some criteria for a subanalytic set to be LNE. It is a
fundamental question to know if the LNE property is a conical property, i.e.,
if it is possible to describe the LNE property of a germ of a subanalytic set
in terms of properties of its link. We answer this question, introducing a new
notion called link Lipschitz normally embedding. We prove that this notion is
equivalent to the LNE notion in the case of sets with connected links. Some
examples and applications of this result are also presented. For example, we
characterize the real Brieskorn's surfaces which are LNE and we give conditions
for a given set to be (or not) LNE in terms of its sections.

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The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc