Some geometric properties of translating solitons in Euclidean space

2018 ◽  
Vol 109 (3) ◽  
Author(s):  
Rafael López
Keyword(s):  
Euclidean Space ◽  
Geometric Properties ◽  
Translating Solitons

scholarly journals Rigidity results and topology at infinity of translating solitons of the mean curvature flow

2017 ◽  
Vol 19 (06) ◽  
pp. 1750002 ◽  
Author(s):  
Debora Impera ◽  
Michele Rimoldi
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Minimal Hypersurfaces ◽  
Rigidity Results ◽  
And Topology ◽  
The Mean ◽  
Translating Solitons

In this paper, we obtain rigidity results and obstructions on the topology at infinity of translating solitons of the mean curvature flow in the Euclidean space. Our approach relies on the theory of [Formula: see text]-minimal hypersurfaces.

Translating solitons foliated by spheres

2017 ◽  
Vol 28 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Daehwan Kim ◽  
Juncheol Pyo
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Higher Dimension ◽  
Translating Soliton ◽  
Surface Of Revolution ◽  
Translating Solitons

In this paper, we consider translating solitons in [Formula: see text] which is foliated by spheres. In three-dimensional Euclidean space, we show that such a translating soliton is a surface of revolution and the axis of revolution is parallel to the translating direction of the translating soliton. We also show that the same result holds for a higher dimension case with a hypersurface foliated by spheres in parallel hyperplanes that are perpendicular to the translating direction.

scholarly journals ON SOME GEOMETRIC PROPERTIES OF QUADRIC SURFACES IN EUCLIDEAN SPACE

2016 ◽  
Vol 38 (3) ◽  
pp. 593-611
Author(s):  
Ahmad T. Ali ◽  
H.S. Abdel Aziz ◽  
Adel H. Sorour
Keyword(s):  
Euclidean Space ◽  
Geometric Properties ◽  
Quadric Surfaces ◽  
Surfaces In Euclidean Space

scholarly journals Generated Surfaces via Inextensible Flows of Curves inR3

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Rawya A. Hussien ◽  
Samah G. Mohamed
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Inextensible Flows ◽  
Curvature And Torsion

We study the inextensible flows of curves in 3-dimensional Euclidean spaceR3. The main purpose of this paper is constructing and plotting the surfaces that are generated from the motion of inextensible curves inR3. Also, we study some geometric properties of those surfaces. We give some examples about the inextensible flows of curves inR3and we determine the curves from their intrinsic equations (curvature and torsion). Finally, we determine and plot the surfaces that are generated by the motion of those curves by using Mathematica 7.

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