On a construction of Burago and Zalgaller

Details On a construction of Burago and Zalgaller On a construction of Burago and Zalgaller

2010-09-29

arxiv.org/abs/1009.5841v1

Mathematics

Differential Geometry

24 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On a construction of Burago and Zalgaller does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On a construction of Burago and Zalgaller, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a construction of Burago and Zalgaller will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-523394