The sharp Sobolev and isoperimetric inequalities split twice |
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Authors: | Jie Xiao |
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Institution: | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada |
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Abstract: | This paper shows that each of the sharp (endpoint) Sobolev inequality and the isoperimetric inequality can be split into two sharp and stronger inequalities through either the 1-variational capacity or the 1-integral affine surface area. Furthermore, some related sharp analytic and geometric inequalities are also explored. |
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Keywords: | primary 26D 46E secondary 52A 53C |
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