The structure of minimal surfaces in CAT(0) spaces

Stadler, Stephan (2021): The structure of minimal surfaces in CAT(0) spaces. In: Journal of the European Mathematical Society, Vol. 23, No. 11: pp. 3521-3554

Abstract

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-Milnor's theorem in the CAT(0) setting.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1435-9855
• Language: English