Piecewise distance preserving maps

Anton Petrunin, A. Yashinski

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This is part of a geometry course held during the Fall 2011 MASS Program at Penn State (www.math.psu.edu/mass/). The online version of these lectures also contains video illustrations, hints, and solutions for most of the exercises, and a minimalistic section covering preliminaries. In the lectures, piecewise distance preserving maps are discussed that act from a 2-dimensional polyhedral space into the plane. Roughly speaking, a polyhedral space is a space that is glued together out of triangles, for example the surface of a polyhedron. If one imagines such a polyhedral space as a paper model, then a piecewise distance preserving map into the plane is essentially a way to fold the model so that it lays flat on a table. Only the 2-dimensional case is considered, to keep things easy to visualize. However, most of the results admit generalizations to higher dimensions. These results are discussed in the Final Remarks, where proper credit and references are given.

Original language English (US) 155-175 21 St. Petersburg Mathematical Journal 27 1 https://doi.org/10.1090/spmj/1381 Published - Jan 1 2016

Fingerprint

Geometry
Polyhedron
Thing
Exercise
Higher Dimensions
Triangle
Table
Fold
Covering
Model
Generalization

All Science Journal Classification (ASJC) codes

• Analysis
• Algebra and Number Theory
• Applied Mathematics

Cite this

Petrunin, Anton ; Yashinski, A. / Piecewise distance preserving maps. In: St. Petersburg Mathematical Journal. 2016 ; Vol. 27, No. 1. pp. 155-175.
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Piecewise distance preserving maps. / Petrunin, Anton; Yashinski, A.

In: St. Petersburg Mathematical Journal, Vol. 27, No. 1, 01.01.2016, p. 155-175.

Research output: Contribution to journalArticle

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