Some properties of minimal surfaces in singular spaces
This paper involves the generalization of minimal surface theory to spaces with singularities. Let be an NPC space, i.e. a metric space of non-positive curvature. We define a (parametric) minimal surface in 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 .
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Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Address at time of publication: Department of Mathematics, Connecticut College, New London, Connecticut 06320
Received by editor(s): March 24, 1998
Received by editor(s) in revised form: November 1, 1998
Published electronically: May 22, 2000
Article copyright: © Copyright 2000 American Mathematical Society