On the Rigidity Theorems for Entire Lagrangian Translating Solitons in Pseudo-Euclidean Space IV

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Yadong Wu ◽  
Ruiwei Xu
Keyword(s):  
Euclidean Space ◽  
Rigidity Theorems ◽  
Translating Solitons

scholarly journals On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space II

2015 ◽  
Vol 26 (09) ◽  
pp. 1550072 ◽  
Author(s):  
R. L. Huang ◽  
R. W. Xu
Keyword(s):  
Euclidean Space ◽  
Convex Function ◽  
Smooth Convex ◽  
Bernstein Type ◽  
Translating Soliton ◽  
Rigidity Theorems ◽  
Vector Formula ◽  
Smooth Convex Function ◽  
Translating Solitons

Let u be a smooth convex function in ℝn and the graph M∇u of ∇u be a space-like translating soliton in pseudo-Euclidean space [Formula: see text] with a translating vector [Formula: see text], then the function u satisfies [Formula: see text] where ai, bi and c are constants. The Bernstein type results are obtained in the course of the arguments.

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.

scholarly journals Rigidity theorems for surfaces in euclidean space

1972 ◽  
Vol 78 (1) ◽  
pp. 72-74 ◽  
Author(s):  
Bang-Yen Chen ◽  
Gerald D. Ludden
Keyword(s):  
Euclidean Space ◽  
Surfaces In Euclidean Space ◽  
Rigidity Theorems

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.

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