THE ISOPERIMETRIC PROBLEM ON PLANES WITH DENSITY

被引：36

作者：

Carroll, Colin ^{[3
]}

Jacob, Adam ^{[2
]}

Quinn, Conor ^{[3
]}

Walters, Robin ^{[1
]}

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[3] Williams Coll, Dept Math & Stat, Williamstown, MA 01267 USA

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2008年 / 78卷 / 02期

基金：

美国国家科学基金会;

关键词：

isoperimetric problem; planes with density; Gauss plane;

D O I：

10.1017/S000497270800052X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the isoperimetric problem in planes with density. In particular, we examine planes with generalized curvature zero. We solve the isoperimetric problem on the plane with density e(x), as well as on the plane with density r(p) for p < 0. The Appendix provides a proof by Robert Bryant that the Gauss plane has a unique closed geodesic.

引用

页码：177 / 197

页数：21

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