홈 editorial content online
Volume 14 (2012)
No 1
Volume 13 (2011)
No 1
Volume 12 (2010)
No 1
Volume 11 (2009)
No 1, No 2
Volume 10 (2008)
No 1, No 2
Volume 9 (2006)
No 1, No 2
Volume 8 (2005)
No 1, No 2
Volume 7 (2004)
No 1, No 2
Volume 6 (2003)
No 1, No 2
Volume 5 (2002)
No 1, No 2
Volume 4 (2001)
No 1, No 2
Volume 3 (2000)
No 1
Volume 2 (1999)
No 1
Volume 1 (1998)
No 1

(2002 / vol.5 / no.2)
On the relative isoperimetric inequality
Jaigyoung Choe
Pages. 65-73     



If $Csubset
n $ is a convex domain and $D$ is a subset of
$
nsim C$, does $D$ satisfy the isoperimetric inequality $
frac{1}{2},n^nomega_nvol(D)^{n-1}leqvol(partial
Dsimpartial C)^n$? Does equality hold if and only if $C=
mathbb{H}$ and $D$ is a half ball with the flat part of its
boundary lying in $partial mathbb{H}$? This inequality is called
the relative isoperimetric inequality. We give three different
proofs of the inequality.



1. Introduction
2. Alexandrov Space
3. Gromov's Method
4. Steiner's Symmetrization
5. Isoperimetric Profile
6. Negatively Curved Surfaces



isoperimetric inequality, convex set, negatively curved manifold



49Q20, 58E35