Korea Institute for Advanced Study, 207-43 Cheongryangri 2-dong, Dongdaemungu, Seoul 130-722, South Korea
Academic Editor: Peter. Y. H. Pang
Copyright © 2010 Juncheol Pyo. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a domain on an -dimensional minimal submanifold in the outside of a convex set in or . The modified volume is introduced by Choe and Gulliver (1992) and we prove a sharp modified relative isoperimetric inequality for the domain , , where is the volume of the unit ball of . For any domain on a minimal surface in the outside convex set in an -dimensional Riemannian manifold, we prove a weak relative isoperimetric inequality , where is an upper bound of sectional curvature of the Riemannian manifold.