Volume 17, Issue 2, June 2010, Pages 145 - 157
Profiles of Inflated Surfaces
Authors
Igor Pak
Department of Mathematics, UCLA, Los Angeles, CA 90095, USA,pak@math.ucla.edu
Jean-Marc Schlenker
Institut de Mathématiques, Université Toulouse III, 31062 Toulouse cedex 9, France,schlenker@math.univ-toulouse.fr
Received 9 February 2009, Accepted 13 August 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S140292511000057XHow to use a DOI?
- Keywords
- Inflated surface; geodesic distance; short embedding; Mylar balloon; convex polyhedron
- Abstract
We study the shape of inflated surfaces introduced in [3] and [12]. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves which we describe explicitly as the solutions of a certain differential equation.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Igor Pak AU - Jean-Marc Schlenker PY - 2021 DA - 2021/01/07 TI - Profiles of Inflated Surfaces JO - Journal of Nonlinear Mathematical Physics SP - 145 EP - 157 VL - 17 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1142/S140292511000057X DO - 10.1142/S140292511000057X ID - Pak2021 ER -