On complete noncompact submanifolds with constant mean curvature and finite total curvature in Euclidean spaces

2006 ◽  
Vol 87 (1) ◽  
pp. 60-71 ◽  
Author(s):  
Senlin Xu ◽  
Qintao Deng
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Total Curvature ◽  
Euclidean Spaces ◽  
Finite Total Curvature

On the compactness of constant mean curvature hypersurfaces with finite total curvature

1999 ◽  
Vol 73 (3) ◽  
pp. 216-222 ◽  
Author(s):  
Manfredo P. do Carmo ◽  
Leung-Fu Cheung ◽  
Walcy Santos
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Total Curvature ◽  
Constant Mean Curvature Hypersurfaces ◽  
Finite Total Curvature

Rotational λ – hypersurfaces in Euclidean spaces

2021 ◽  
Vol 30 (1) ◽  
pp. 29-40
Author(s):  
KADRI ARSLAN ◽  
ALIM SUTVEREN ◽  
BETUL BULCA
Keyword(s):  
Present Article ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Special Solution ◽  
Euclidean Spaces ◽  
Self Similar ◽  
The Mean ◽  
Similar Flows

Self-similar flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, \lambda -hypersurfaces are the generalization of self-similar hypersurfaces. In the present article we consider \lambda -hypersurfaces in Euclidean spaces which are the generalization of self-shrinkers. We obtained some results related with rotational hypersurfaces in Euclidean 4-space \mathbb{R}^{4} to become self-shrinkers. Furthermore, we classify the general rotational \lambda -hypersurfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational \lambda -hypersurfaces in \mathbb{R}^{4}.

scholarly journals Index and total curvature of surfaces with constant mean curvature

1990 ◽  
Vol 110 (4) ◽  
pp. 1009-1009 ◽  
Author(s):  
Manfredo P. do Carmo ◽  
Alexandre M. Da Silveira
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Total Curvature

scholarly journals On regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces

2021 ◽  
pp. 1-8
Author(s):  
Alexandre Paiva Barreto ◽  
Francisco Fontenele ◽  
Luiz Hartmann
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Euclidean Spaces ◽  
Algebraic Hypersurfaces ◽  
Odd Degree

We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space $\mathbb {R}^{n+1},\,\;n\geq 2,$ defined by polynomials of odd degree. Also we prove that the hyperspheres and the round cylinders are the only regular algebraic hypersurfaces with non-zero constant mean curvature in $\mathbb {R}^{n+1}, n\geq 2,$ defined by polynomials of degree less than or equal to three. These results give partial answers to a question raised by Barbosa and do Carmo.

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