Some properties of minimal surfaces in singular spaces

Mese, Chikako

doi:10.1090/S0002-9947-00-02481-8

Some properties of minimal surfaces in singular spaces
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Trans. Amer. Math. Soc. 352 (2000), 3957-3969 Request permission

Abstract:

This paper involves the generalization of minimal surface theory to spaces with singularities. Let $X$ be an NPC space, i.e. a metric space of non-positive curvature. We define a (parametric) minimal surface in $X$ as a conformal energy minimizing map. Using this definition, many properties of classical minimal surfaces can also be observed for minimal surfaces in this general setting. In particular, we will prove the boundary monotonicity property and the isoperimetric inequality for minimal surfaces in $X$.

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