Minimal surfaces in three dimensional Lorentzian Heisenberg group

2013 ◽  
Vol 55 (1) ◽  
pp. 1-23
Author(s):  
Essin Turhan ◽  
Gülden Altay
Keyword(s):  
Heisenberg Group ◽  
Minimal Surfaces ◽  
Three Dimensional

scholarly journals Ruled minimal surfaces in the three-dimensional Heisenberg group

2013 ◽  
Vol 261 (2) ◽  
pp. 477-496 ◽  
Author(s):  
Heayong Shin ◽  
Young Wook Kim ◽  
Sung-Eun Koh ◽  
Hyung Yong Lee ◽  
Seong-Deog Yang
Keyword(s):  
Heisenberg Group ◽  
Minimal Surfaces ◽  
Three Dimensional

scholarly journals A loop group method for minimal surfaces in the three-dimensional Heisenberg group

2016 ◽  
Vol 20 (3) ◽  
pp. 409-448
Author(s):  
Josef F. Dorfmeister ◽  
Jun-Ichi Inoguchi ◽  
Shimpei Kobayashi
Keyword(s):  
Heisenberg Group ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Loop Group ◽  
Group Method

scholarly journals The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group

2014 ◽  
Vol 195 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Adriana A. Cintra ◽  
Francesco Mercuri ◽  
Irene I. Onnis
Keyword(s):  
Lie Group ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Björling Problem

scholarly journals Einstein–Weyl geometry, dispersionless Hirota equation and Veronese webs

2014 ◽  
Vol 157 (1) ◽  
pp. 139-150 ◽  
Author(s):  
MACIEJ DUNAJSKI ◽  
WOJCIECH KRYŃSKI
Keyword(s):  
Heisenberg Group ◽  
Twistor Space ◽  
Three Dimensional ◽  
Poisson Structures ◽  
Weyl Geometry ◽  
Hirota Equation ◽  
Five Dimensions ◽  
Dispersionless Hirota Equation

AbstractWe exploit the correspondence between the three–dimensional Lorentzian Einstein–Weyl geometries of the hyper–CR type and the Veronese webs to show that the former structures are locally given in terms of solutions to the dispersionless Hirota equation. We also demonstrate how to construct hyper–CR Einstein–Weyl structures by Kodaira deformations of the flat twistor space$T\mathbb{CP}^1$, and how to recover the pencil of Poisson structures in five dimensions illustrating the method by an example of the Veronese web on the Heisenberg group.

Surfaces in the three-dimensional Heisenberg group on which the Gauss map has bounded Jacobian

2011 ◽  
Vol 89 (5-6) ◽  
pp. 746-748 ◽  
Author(s):  
A. A. Borisenko ◽  
E. V. Petrov
Keyword(s):  
Heisenberg Group ◽  
Three Dimensional ◽  
Gauss Map

scholarly journals Geometric convergence results for closed minimal surfaces via bubbling analysis

2021 ◽  
Vol 61 (1) ◽  
Author(s):  
Lucas Ambrozio ◽  
Reto Buzano ◽  
Alessandro Carlotto ◽  
Ben Sharp
Keyword(s):  
Minimal Surfaces ◽  
Sharp Estimate ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Global Character ◽  
Multiplicity One ◽  
Convergence Results ◽  
Geometric Convergence ◽  
Number Of Ends

AbstractWe present some geometric applications, of global character, of the bubbling analysis developed by Buzano and Sharp for closed minimal surfaces, obtaining smooth multiplicity one convergence results under upper bounds on the Morse index and suitable lower bounds on either the genus or the area. For instance, we show that given any Riemannian metric of positive scalar curvature on the three-dimensional sphere the class of embedded minimal surfaces of index one and genus $$\gamma $$ γ is sequentially compact for any $$\gamma \ge 1$$ γ ≥ 1 . Furthemore, we give a quantitative description of how the genus drops as a sequence of minimal surfaces converges smoothly, with mutiplicity $$m\ge 1$$ m ≥ 1 , away from finitely many points where curvature concentration may happen. This result exploits a sharp estimate on the multiplicity of convergence in terms of the number of ends of the bubbles that appear in the process.

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