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Some properties of minimal surfaces in singular spaces

Author(s): Chikako Mese
Journal: Trans. Amer. Math. Soc. 352 (2000), 3957-3969.
MSC (1991): Primary 58E12
Posted: May 22, 2000
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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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Additional Information:

Chikako Mese
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
Email: cmes@conncoll.edu

DOI: 10.1090/S0002-9947-00-02481-8
PII: S 0002-9947(00)02481-8
Received by editor(s): March 24, 1998
Received by editor(s) in revised form: November 1, 1998
Posted: May 22, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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