The structure of singular spaces of dimension 2 (Q1819140)

In the present paper the author studies the structure of locally compact metric spaces of Hausdorff dimension \(2\). If such a space has non-positive curvature and a local cone structure then every simple closed curve bounds a conformal disk. If a metric on a surface has non-positive curvature and its topology is equivalent to the surface topology then this gives a structure of a Riemann surface. The construction of conformal disks in these spaces is based on the theory of minimal surfaces.