Curvature Estimates for some Minimal Surfaces

1988 ◽  
pp. 87-100 ◽  
Author(s):  
Walter Hengartner ◽  
Glenn Schober
Keyword(s):  
Minimal Surfaces ◽  
Curvature Estimates

scholarly journals The Geometry of Minimal Surfaces of Finite Genus I: Curvature Estimates and Quasiperiodicity

2004 ◽  
Vol 66 (1) ◽  
pp. 1-45 ◽  
Author(s):  
William H. Meeks III ◽  
Joaquín Pérez ◽  
Antonio Ros
Keyword(s):  
Minimal Surfaces ◽  
Curvature Estimates ◽  
Finite Genus

scholarly journals A Family of Minimal Surfaces and Univalent Planar Harmonic Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Michael Dorff ◽  
Stacey Muir
Keyword(s):  
Minimal Surfaces ◽  
Parameter Family ◽  
Harmonic Mappings ◽  
Continuous Transformation ◽  
Identification Process ◽  
Curvature Estimates ◽  
Convex In One Direction ◽  
Planar Harmonic Mappings ◽  
Small Shear ◽  
Two Parameter

We present a two-parameter family of minimal surfaces constructed by lifting a family of planar harmonic mappings. In the process, we use the Clunie and Sheil-Small shear construction for planar harmonic mappings convex in one direction. This family of minimal surfaces, through a continuous transformation, has connections with three well-known surfaces: Enneper’s surface, the wavy plane, and the helicoid. Moreover, the identification process used to recognize the surfaces provides a connection to surfaces that give tight bounds on curvature estimates first studied in a 1988 work by Hengartner and Schober.

THE EXISTENCE OF SURFACE PATCHES FOR PERIODIC MINIMAL SURFACES

1990 ◽  
Vol 51 (C7) ◽  
pp. C7-265-C7-271 ◽  
Author(s):  
J. C.C. NITSCHE
Keyword(s):  
Minimal Surfaces ◽  
Surface Patches
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