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Estimates in surfaces with positive constant Gauss curvature


Authors: José A. Gálvez and Antonio Martínez
Journal: Proc. Amer. Math. Soc. 128 (2000), 3655-3660
MSC (2000): Primary 53A05
DOI: https://doi.org/10.1090/S0002-9939-00-05805-6
Published electronically: June 7, 2000
MathSciNet review: 1778281
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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.


References [Enhancements On Off] (What's this?)

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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: https://doi.org/10.1090/S0002-9939-00-05805-6
Keywords: $K$-surfaces, height, area, volume
Received by editor(s): February 24, 1999
Published electronically: June 7, 2000
Additional Notes: This research was partially supported by DGICYT Grant No. PB97-0785.
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society

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