Some properties of minimal surfaces in singular spaces

Author:
Chikako Mese

Journal:
Trans. Amer. Math. Soc. **352** (2000), 3957-3969

MSC (1991):
Primary 58E12

Published electronically:
May 22, 2000

MathSciNet review:
1661254

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Abstract | References | Similar Articles | Additional Information

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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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:
http://dx.doi.org/10.1090/S0002-9947-00-02481-8

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