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Register a new userConformal deformations of CAT(0) spaces
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We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial deformations.
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We prove that a minimal disc in a CAT(0) space is a local embedding away from a finite set of branch points. On the way we establish several basic properties of minimal surfaces: monotonicity of area densities, density bounds, limit theorems and the existence of tangent maps. As an application, we prove Fary-Milnors theorem in the CAT(0) setting.
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