The sharp Sobolev and isoperimetric inequalities split twice

• Autores: Jie Xiao
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 211, Nº 2, 2007, págs. 417-435
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.08.006
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• Resumen

  • 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