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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Piecewise distance preserving maps


Authors: A. Petrunin and A. Yashinski
Translated by: the authors
Original publication: Algebra i Analiz, tom 27 (2015), nomer 1.
Journal: St. Petersburg Math. J. 27 (2016), 155-175
MSC (2010): Primary 52B70
DOI: https://doi.org/10.1090/spmj/1381
Published electronically: December 7, 2015
MathSciNet review: 3443270
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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.


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Additional Information

A. Petrunin
Affiliation: Mathematics Department, Penn State University, University Park, Pennsylvania 16802
Email: anton.petrunin@gmail.com

A. Yashinski
Affiliation: Mathematics Department, Penn State University, University Park, Pennsylvania 16802
Email: allan@math.hawaii.edu

DOI: https://doi.org/10.1090/spmj/1381
Keywords: Polyhedral space, piecewise distance preserving maps, piecewise linear maps
Received by editor(s): May 25, 2014
Published electronically: December 7, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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