Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a construction of Burago and Zalgaller   The purpose of this note is to scrutinize the proof of Burago and Zalgaller
regarding the existence of $PL$ isometric embeddings of $PL$ compact surfaces
into $\mathbb{R}^3$. We conclude that their proof does not admit a direct
extension to higher dimensions. Moreover, we show that, in general, $PL$
manifolds of dimension $n \geq 3$ admit no nontrivial $PL$ embeddings in
$\mathbb{R}^{n+1}$ that are close to conformality. We also extend the result of
Burago and Zalgaller to a large class of noncompact $PL$ 2-manifolds. The
relation between intrinsic and extrinsic curvatures is also examined, and we
propose a $PL$ version of the Gauss compatibility equation for smooth surfaces.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph