scholarly journals Geometric inequalities involving mean curvature for closed surfaces

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Tatsuya Miura
Keyword(s):  
Mean Curvature ◽  
Geometric Inequalities ◽  
Closed Surfaces

Integral criteria for closed surfaces with constant mean curvature

2007 ◽  
Vol 463 (2081) ◽  
pp. 1199-1210
Author(s):  
Luca Guzzardi ◽  
Epifanio G Virga
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Second Variation ◽  
Closed Surfaces ◽  
Area Functional ◽  
Symmetric Surface ◽  
The Second Variation ◽  
Integral Identities

We propose three integral criteria that must be satisfied by all closed surfaces with constant mean curvature immersed in the three-dimensional Euclidean space. These criteria are integral identities that follow from requiring the second variation of the area functional to be invariant under rigid displacements. We obtain from them a new proof of the old result by Delaunay, to the effect that the sphere is the only closed axis-symmetric surface.

scholarly journals An integral formula in Kähler geometry with applications

2016 ◽  
Vol 19 (05) ◽  
pp. 1650063 ◽  
Author(s):  
Xiaodong Wang
Keyword(s):  
Mean Curvature ◽  
Integral Formula ◽  
Kähler Manifold ◽  
Holomorphic Extension ◽  
Geometric Inequalities ◽  
Kahler Geometry ◽  
Cr Functions ◽  
Kahler Manifold ◽  
Extension Of Cr Functions

We establish an integral formula on a smooth, precompact domain in a Kähler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula, we also prove some geometric inequalities when the boundary has positive Hermitian mean curvature.

scholarly journals Harmonic mean curvature flow and geometric inequalities

2020 ◽  
Vol 375 ◽  
pp. 107393
Author(s):  
Ben Andrews ◽  
Yingxiang Hu ◽  
Haizhong Li
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Harmonic Mean ◽  
Geometric Inequalities
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