scholarly journals Nontrivial minimal surfaces in a hyperbolic Randers space

2016 ◽  
Vol 290 (4) ◽  
pp. 570-582
Author(s):  
Ningwei Cui ◽  
Yi-Bing Shen
Keyword(s):  
Minimal Surfaces ◽  
Randers Space

Helicoidal Minimal Surfaces in a Finsler Space of Randers Type

2014 ◽  
Vol 57 (4) ◽  
pp. 765-779 ◽  
Author(s):  
Rosângela Maria da Silva ◽  
Keti Tenenblat
Keyword(s):  
Differential Equation ◽  
Minimal Surface ◽  
Minimal Surfaces ◽  
Finsler Space ◽  
Volume Form ◽  
Randers Metric ◽  
Euclidean Metric ◽  
Randers Space ◽  
Open Region ◽  
Fixed Axis

AbstractWe consider the Finsler space obtained by perturbing the Euclidean metric of ℝ3 by a rotation. It is the open region of ℝ3 bounded by a cylinder with a Randers metric. Using the Busemann–Hausdorff volume form, we obtain the differential equation that characterizes the helicoidal minimal surfaces in . We prove that the helicoid is a minimal surface in only if the axis of the helicoid is the axis of the cylinder. Moreover, we prove that, in the Randers space , the only minimal surfaces in the Bonnet family with fixed axis Ox̄3 are the catenoids and the helicoids.

Remarks on minimal surfaces in a 3-dimensional Randers space

2018 ◽  
Vol 109 (1) ◽  
Author(s):  
Zhong-Hua Hou ◽  
Yong-Nan Liu
Keyword(s):  
Minimal Surfaces ◽  
3 Dimensional ◽  
Randers Space

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.

Minimal Surfaces from a Complex Analytic Viewpoint

2021 ◽  
Author(s):  
Antonio Alarcón ◽  
Franc Forstnerič ◽  
Francisco J. López
Keyword(s):  
Minimal Surfaces

scholarly journals The Adjunction Inequality for Weyl-Harmonic Maps

2020 ◽  
Vol 7 (1) ◽  
pp. 129-140
Author(s):  
Robert Ream
Keyword(s):  
Minimal Surfaces ◽  
Twistor Space ◽  
Harmonic Maps ◽  
Holomorphic Curves ◽  
Weyl Connection ◽  
Almost Kähler ◽  
Conformal Manifolds

AbstractIn this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequality\chi \left( {{T_f}\sum } \right) + \chi \left( {{N_f}\sum } \right) \le \pm {c_1}\left( {f*{T^{\left( {1,0} \right)}}M} \right).The ±J-holomorphic curves are automatically Weyl-minimal and satisfy the corresponding equality. These results generalize results of Eells-Salamon and Webster for minimal surfaces in Kähler 4-manifolds as well as their extension to almost-Kähler 4-manifolds by Chen-Tian, Ville, and Ma.

scholarly journals Structural Models Based on Minimal Surfaces and Geodesics

2021 ◽  
Author(s):  
Francisco Gonzalez-Quintial ◽  
Andres Martin-Pastor
Keyword(s):  
Minimal Surfaces ◽  
Structural Models
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