1. CJM 1997 (vol 49 pp. 1162)
|Isoperimetric inequalities on surfaces of constant curvature |
In this paper we introduce the concepts of hyperbolic and elliptic areas and prove uncountably many new geometric isoperimetric inequalities on the surfaces of constant curvature.
Keywords:Gaussian curvature, Gauss-Bonnet theorem, polygon, pseudo-polygon, pseudo-perimeter, hyperbolic surface, Heron's formula, analytic and geometric isoperimetric inequalities
Categories:51M10, 51M25, 52A40, 53C20