Isoperimetric problem and minimal surfaces in the Heisenberg group

2014 ◽  
pp. 57-129 ◽  
Author(s):  
Roberto Monti
Keyword(s):  
Heisenberg Group ◽  
Minimal Surfaces ◽  
Isoperimetric Problem

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 A partial solution of the isoperimetric problem for the Heisenberg group

2008 ◽  
Vol 20 (1) ◽  
Author(s):  
Donatella Danielli ◽  
Nicola Garofalo ◽  
Duy-Minh Nhieu
Keyword(s):  
Heisenberg Group ◽  
Isoperimetric Problem ◽  
Partial Solution

scholarly journals Properly embedded and immersed minimal surfaces in the Heisenberg group

2004 ◽  
Vol 70 (3) ◽  
pp. 507-520 ◽  
Author(s):  
Jih-Hsin Cheng ◽  
Jenn-Fang Hwang
Keyword(s):  
Heisenberg Group ◽  
Minimal Surface ◽  
Explicit Expression ◽  
Minimal Surfaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Minimal Graphs ◽  
3 Dimensional ◽  
Necessary And Sufficient ◽  
Band Type

We study properly embedded and immersed p(pseudohermitian)-minimal surfaces in the 3-dimensional Heisenberg group. From the recent work of Cheng, Hwang, Malchiodi, and Yang, we learn that such surfaces must be ruled surfaces. There are two types of such surfaces: band type and annulus type according to their topology. We givn an explicit expression for these surfaces. Among band types there is a class of properly embedded p-minimal surfaces of so called helicoid type. We classify all the helicoid type p-minimal surfaces. This class of p-minimal surfaces includes all the entire p-minimal graphs (except contact planes) over any plane. Moreover, we give a necessary and sufficient condition for such a p-minimal surface to have no singular points. For general complete immersed p-minimal surfaces, we prove a half space theorem and give a criterion for the properness.

scholarly journals Minimal Surfaces in the Heisenberg Group

2004 ◽  
Vol 104 (1) ◽  
pp. 201-231 ◽  
Author(s):  
Scott D. Pauls
Keyword(s):  
Heisenberg Group ◽  
Minimal Surfaces
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