Isoperimetric inequality for higher-dimensional black holes

The initial data sets for the five-dimensional Einstein equation have been examined. The system is designed such that the black hole (similar or equal toS(3)) or the black ring (similar or equal toS(2)xS(1)) can be found. We have found that the typical length of the horizon can become arbitrarily large but the area of characteristic closed two-dimensional submanifold of the horizon is bounded above by the typical mass scale. We conjecture that the isoperimetric inequality for black holes in n-dimensional space is given by V(n-2)less than or similar toGM, where Vn-2 denotes the volume of a typical closed (n-2)-section of the horizon and M is typical mass scale, rather than Cless than or similar to(GM)(1/(n-2)) in terms of the hoop length C, which holds only when n=3.