Estimates in surfaces with positive constant Gauss curvature

Gálvez, José; Martínez, Antonio

doi:10.1090/S0002-9939-00-05805-6

Estimates in surfaces with positive constant Gauss curvature
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by José A. Gálvez and Antonio Martínez PDF

Proc. Amer. Math. Soc. 128 (2000), 3655-3660 Request permission

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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