Affine isoperimetric inequalities for piecewise linear surfaces
| dc.creator | Hass, Joel | |
| dc.creator | Lagarias, Jeffrey C. | |
| dc.date | 2002-02-18 | |
| dc.date.accessioned | 2026-07-07T04:46:32Z | |
| dc.date.available | 2026-07-07T04:46:32Z | |
| dc.description | This paper considers affine analogues of the isoperimetric inequality in the sense of piecewise linear topology. Given a closed polygon P embedded in R^d having n edges, we give upper and lower bounds for the minimal number of triangles needed to forma triangulated embedded orientable surface in R^d having P as its geometric boundary. The most interesting case is dimension dimension 3, where we give an upper bound of 7 n^2 triangles, and a lower bound for some polygons P that require at least 1/2 n^2 triangles. In dimension 2 and dimensions 5 and above one needs only O(n) triangles. The case of dimension 4 is not completely resolved. | |
| dc.description | 14 pages latex, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0202179 | |
| dc.identifier | http://arxiv.org/abs/math/0202179 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63370 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53A10 (primary); 52B60, 57Q15 (secondary) | |
| dc.title | Affine isoperimetric inequalities for piecewise linear surfaces | |
| dc.type | text |