The Minimal Perimeter of a Log-Concave Function
Inspired by the equivalence between isoperimetric inequality and Sobolev inequality, we provide a new connection between geometry and analysis. We define the minimal perimeter of a log-concave function and establish a characteristic theorem of this extremal problem for log-concave functions analogou...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1365 |
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doaj-8be384a3feb64cebb23c34ecfee970732020-11-25T03:34:43ZengMDPI AGMathematics2227-73902020-08-0181365136510.3390/math8081365The Minimal Perimeter of a Log-Concave FunctionNiufa Fang0Zengle Zhang1Chern Institute of Mathematics, Nankai University, Tianjin 300071, ChinaKey Laboratory of Group and Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing 402160, ChinaInspired by the equivalence between isoperimetric inequality and Sobolev inequality, we provide a new connection between geometry and analysis. We define the minimal perimeter of a log-concave function and establish a characteristic theorem of this extremal problem for log-concave functions analogous to convex bodies.https://www.mdpi.com/2227-7390/8/8/1365isoperimetric problemminimal perimeterlog-concave functionsisotropic measure |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Niufa Fang Zengle Zhang |
| spellingShingle |
Niufa Fang Zengle Zhang The Minimal Perimeter of a Log-Concave Function Mathematics isoperimetric problem minimal perimeter log-concave functions isotropic measure |
| author_facet |
Niufa Fang Zengle Zhang |
| author_sort |
Niufa Fang |
| title |
The Minimal Perimeter of a Log-Concave Function |
| title_short |
The Minimal Perimeter of a Log-Concave Function |
| title_full |
The Minimal Perimeter of a Log-Concave Function |
| title_fullStr |
The Minimal Perimeter of a Log-Concave Function |
| title_full_unstemmed |
The Minimal Perimeter of a Log-Concave Function |
| title_sort |
minimal perimeter of a log-concave function |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2020-08-01 |
| description |
Inspired by the equivalence between isoperimetric inequality and Sobolev inequality, we provide a new connection between geometry and analysis. We define the minimal perimeter of a log-concave function and establish a characteristic theorem of this extremal problem for log-concave functions analogous to convex bodies. |
| topic |
isoperimetric problem minimal perimeter log-concave functions isotropic measure |
| url |
https://www.mdpi.com/2227-7390/8/8/1365 |
| work_keys_str_mv |
AT niufafang theminimalperimeterofalogconcavefunction AT zenglezhang theminimalperimeterofalogconcavefunction AT niufafang minimalperimeterofalogconcavefunction AT zenglezhang minimalperimeterofalogconcavefunction |
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