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Bonnesen-style Wulff isoperimetric inequality.
Zengle Zhang1, Jiazu Zhou1,2
1School of Mathematics and Statistics, Southwest University, Chongqing, 400715 People's Republic of China.
Journal of Inequalities and Applications
|March 4, 2017
Summary
This study extends the classical isoperimetric inequality by establishing new Bonnesen-style and reverse Bonnesen-style Wulff isoperimetric inequalities. These findings build upon and generalize existing inequalities in geometric measure theory.
Area of Science:
- Geometric measure theory
- Differential geometry
Background:
- The classical isoperimetric inequality relates the perimeter and area of shapes.
- The Wulff isoperimetric inequality is a generalization of the classical form.
Purpose of the Study:
- To establish novel Bonnesen-style Wulff isoperimetric inequalities.
- To establish novel reverse Bonnesen-style Wulff isoperimetric inequalities.
Main Methods:
- Utilizing techniques from geometric analysis.
- Applying methods related to isoperimetric problems.
Main Results:
- New Bonnesen-style Wulff isoperimetric inequalities were derived.
- New reverse Bonnesen-style Wulff isoperimetric inequalities were established.
- The derived inequalities generalize previously known results.
Conclusions:
- The study successfully extends the theory of Wulff isoperimetric inequalities.
- The established inequalities offer new insights into geometric measure theory.
Keywords:
Bonnesen-style Wulff isoperimetric inequalityWulff flowWulff isoperimetric inequalityreverse Bonnesen-style Wulff isoperimetric inequalityMore Related Videos
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