Laguerre minimal surfaces via congruence of lines

2012 ◽  
Vol 44 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Rafaela F. do Prado ◽  
Pedro Roitman
Keyword(s):  
Minimal Surfaces ◽  
Laguerre Minimal Surfaces

Complete Laguerre minimal surfaces in R3

2013 ◽  
Vol 92 ◽  
pp. 1-12 ◽  
Author(s):  
Juan A. Aledo ◽  
José A. Gálvez ◽  
Victorino Lozano
Keyword(s):  
Minimal Surfaces ◽  
Laguerre Minimal Surfaces

Laguerre minimal surfaces in ℝ3

2008 ◽  
Vol 24 (11) ◽  
pp. 1861-1870 ◽  
Author(s):  
Yu Ping Song ◽  
Chang Ping Wang
Keyword(s):  
Minimal Surfaces ◽  
Laguerre Minimal Surfaces

scholarly journals Biharmonic Maps and Laguerre Minimal Surfaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yusuf Abu Muhanna ◽  
Rosihan M. Ali
Keyword(s):  
Minimal Surface ◽  
Gaussian Curvature ◽  
Minimal Surfaces ◽  
Complete Characterization ◽  
Necessary Condition ◽  
Biharmonic Maps ◽  
Laguerre Minimal Surfaces ◽  
Laguerre Minimal Surface ◽  
Sufficient And Necessary Condition

A Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surfaceΦis its associated surfaceΨ=1+u2Φ, whereulies in the unit disk. In this paper, the projection of the surfaceΨassociated to a Laguerre minimal surface is shown to be biharmonic. A complete characterization ofΨis obtained under the assumption that the corresponding isotropic map of the Laguerre minimal surface is harmonic. A sufficient and necessary condition is also derived forΨto be a graph. Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given.

scholarly journals Laguerre minimal surfaces, isotropic geometry and linear elasticity

2008 ◽  
Vol 31 (4) ◽  
pp. 391-419 ◽  
Author(s):  
Helmut Pottmann ◽  
Philipp Grohs ◽  
Niloy J. Mitra
Keyword(s):  
Linear Elasticity ◽  
Minimal Surfaces ◽  
Laguerre Minimal Surfaces

scholarly journals Ruled Laguerre minimal surfaces

2011 ◽  
Vol 272 (1-2) ◽  
pp. 645-674 ◽  
Author(s):  
Mikhail Skopenkov ◽  
Helmut Pottmann ◽  
Philipp Grohs
Keyword(s):  
Minimal Surfaces ◽  
Laguerre Minimal Surfaces

scholarly journals On different notions of calibrations for minimal partitions and minimal networks in ℝ2

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Marcello Carioni ◽  
Alessandra Pluda
Keyword(s):  
Minimal Surfaces ◽  
Steiner Problem ◽  
Minimal Networks

Abstract Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of the Steiner problem in several variants. Our goal is to compare the different notions of calibrations for the Steiner problem and for planar minimal partitions that are already present in the literature. The paper is then complemented with remarks on the convexification of the problem, on nonexistence of calibrations and on calibrations in families.

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