Total Mean Curvature of Immersed Surfaces in E m

1976 ◽  
Vol 218 ◽  
pp. 333
Author(s):  
Bang-Yen Chen
Keyword(s):  
Mean Curvature ◽  
Immersed Surfaces ◽  
Total Mean Curvature

On the total mean curvature of a compact space-like submanifold in Lorentz–Minkowski spacetime

2017 ◽  
Vol 148 (1) ◽  
pp. 199-210 ◽  
Author(s):  
Oscar Palmas ◽  
Francisco J. Palomo ◽  
Alfonso Romero
Keyword(s):  
Euclidean Space ◽  
Compact Space ◽  
Upper Bound ◽  
Mean Curvature ◽  
Light Cone ◽  
Minkowski Spacetime ◽  
Totally Umbilical ◽  
Total Mean Curvature ◽  
Lower Estimation ◽  
Compact Submanifold

By means of several counterexamples, the impossibility to obtain an analogue of the Chen lower estimation for the total mean curvature of any compact submanifold in Euclidean space for the case of compact space-like submanifolds in Lorentz–Minkowski spacetime is shown. However, a lower estimation for the total mean curvature of a four-dimensional compact space-like submanifold that factors through the light cone of six-dimensional Lorentz–Minkowski spacetime is proved by using a technique completely different from Chen's original one. Moreover, the equality characterizes the totally umbilical four-dimensional round spheres in Lorentz–Minkowski spacetime. Finally, three applications are given. Among them, an extrinsic upper bound for the first non-trivial eigenvalue of the Laplacian of the induced metric on a four-dimensional compact space-like submanifold that factors through the light cone is proved.

scholarly journals An integral formula for the total mean curvature matrix

2015 ◽  
Vol 68 ◽  
pp. 1-17 ◽  
Author(s):  
Chunna Zeng ◽  
Wenxue Xu ◽  
Jiazu Zhou ◽  
Lei Ma
Keyword(s):  
Mean Curvature ◽  
Integral Formula ◽  
Total Mean Curvature

scholarly journals On the Minimization of Total Mean Curvature

2015 ◽  
Vol 26 (4) ◽  
pp. 2729-2750 ◽  
Author(s):  
J. Dalphin ◽  
A. Henrot ◽  
S. Masnou ◽  
T. Takahashi
Keyword(s):  
Mean Curvature ◽  
Total Mean Curvature

scholarly journals On the Kinematic Formula of the Total Mean Curvature Matrix

2017 ◽  
Vol 21 (1) ◽  
pp. 43-54
Author(s):  
Chunna Zeng ◽  
Lei Ma ◽  
Yin Tong
Keyword(s):  
Mean Curvature ◽  
Kinematic Formula ◽  
Total Mean Curvature
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