The isodiametric problem and other inequalities in the constant curvature 2-spaces

In this paper we prove several new inequalities for centrally symmetric convex bodies in the 2-dimensional spaces of constant curvature κ , which have their analog in the plane. Thus, when κ tends to 0, the classical planar inequalities will be obtained. For instance, we get the relation between the...

Full description

Saved in:
Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2015-09, Vol.109 (2), p.315-325
Main Authors: Hernández Cifre, María A., Martínez Fernández, Antonio R.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we prove several new inequalities for centrally symmetric convex bodies in the 2-dimensional spaces of constant curvature κ , which have their analog in the plane. Thus, when κ tends to 0, the classical planar inequalities will be obtained. For instance, we get the relation between the perimeter and the diameter of a symmetric convex body (Rosenthal–Szasz inequality) which, together with the well-known spherical/hyperbolic isoperimetric inequality, allows to solve the isodiametric problem. The analogs to other classical planar relations are also proved.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-014-0183-5