Piecewise distance preserving maps

A. Petrunin, A. Yashinski

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
Pages (from-to)155-175
Number of pages21
JournalSt. Petersburg Mathematical Journal
Issue number1
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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