Resumen de A new family of parametric isoperimetric inequalities

Xiang Gao, Jin Mu Song, Hai Yong Li

• 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.