A discussion of the isoperimetric problem on spheres withrotational and equatorial symmetry and monotone Gausscurvature

• Main Authors: Yi-Te Hong, 洪亦德
• Other Authors: Fei-Tsen Liang
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/25540757290019922161

碩士 === 臺灣大學 === 數學研究所 === 98 === In the thesis we follow the demonstration of Prof. M. Ritoré to solve the isoperimetric problem on roatationally and equatorially symmetric spheres with monotone Gauss curvature from the poles. We first classify all the curves with constant geodesic curvature on a sphere with the above properties. Then we apply Sturm''s comparison theorem successively to get the final only possible curve enclosing an isoperimetric domain. On regions with constant Gauss curvature we also invoke the Bol-Fiala inequality to conclude that inside such regions a geodesic circle has the minimal length encircling a domain with a given area.