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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Surfaces with harmonic inverse
mean curvature in space forms


Author: Atsushi Fujioka
Journal: Proc. Amer. Math. Soc. 127 (1999), 3021-3025
MSC (1991): Primary 53A10; Secondary 53A05
Published electronically: April 23, 1999
MathSciNet review: 1600144
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Abstract: We define surfaces with harmonic inverse mean curvature in space forms and generalize a theorem due to Lawson by which surfaces of constant mean curvature in one space form isometrically correspond to those in another. We also obtain an immersion formula, which gives a deformation family for these surfaces.


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Additional Information

Atsushi Fujioka
Affiliation: Department of Mathematics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192 Japan
Address at time of publication: Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192 Japan
Email: fujioka@kappa.s.kanazawa-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04837-6
PII: S 0002-9939(99)04837-6
Keywords: Constant mean curvature surfaces, surfaces with prescribed mean curvature
Received by editor(s): March 20, 1997
Received by editor(s) in revised form: December 4, 1997
Published electronically: April 23, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society