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Estimates in surfaces with positive constant Gauss curvature

Author(s): José A. Gálvez; Antonio Martínez
Journal: Proc. Amer. Math. Soc. 128 (2000), 3655-3660.
MSC (2000): Primary 53A05
Posted: June 7, 2000
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Abstract:

We give optimal bounds of the height, curvature, area and volume of $K$-surfaces in $\mathbb{R} ^3$ bounding a planar curve. The spherical caps are characterized as the unique $K$-surfaces achieving these bounds.

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Additional Information:

José A. Gálvez
Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: jagalvez@goliat.ugr.es

Antonio Martínez
Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: amartine@goliat.ugr.es

DOI: 10.1090/S0002-9939-00-05805-6
PII: S 0002-9939(00)05805-6
Keywords: $K$-surfaces, height, area, volume
Received by editor(s): February 24, 1999
Posted: June 7, 2000
Additional Notes: This research was partially supported by DGICYT Grant No. PB97-0785.
Communicated by: Christopher Croke
Copyright of article: Copyright 2000, American Mathematical Society

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