A new family of parametric isoperimetric inequalities

• Xiang Gao ^[1] ; Jin-Mu Song ^[1] ; Hai-Yong Li ^[1]
  1. [1] Ocean University of China

     Ocean University of China

     China

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 55, Nº. 1, 2014, págs. 1-18
• Idioma: inglés
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• Resumen

  • In this paper, we deal with isoperimetric-type inequalities for the closed convex curve in the Euclidean plane R2. In fact we establish a family of parametric inequalities involving some geometric functionals associated to the given closed convex curve with a simple Fourier series proof. Furthermore, we investigate some stability properties of such inequalities.