^{*}

Dedicated to Gary Gibbons on the occasion of his 75th birthday.

Author to whom any correspondence should be addressed.

We use an isometric embedding of the cross-over surface of the outer horizon of a rapidly rotating Kerr black hole in a hyperbolic space to compute the quasi-local mass of the horizon for any allowed value of the spin parameter ^{2}. The mass is monotonically decreasing from twice the ADM mass at