NONPOSITIVELY CURVED SINGULAR SURFACES CONTAINING BALLS WITH INFINITE AREA

Yong-Il Kim (Korea) and Doohann Lee (Korea)

Received December 14, 2007

Abstract

We construct a 2-dimensional length space of nonpositive curvature in the sense of Alexandrov with a property that balls centered at a fixed point of any radius have infinite 2-dimensional Hausdorff measure and infinite circumference.

Keywords and phrases: singular Hadamard space, isoperimetric inequality.