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Barchiesi, Marco; Cagnetti, Filippo; Fusco, Nicola (2013)
Publisher: European Mathematical Society Publishing House
Languages: English
Types: Article
Subjects: QA299

Classified by OpenAIRE into

arxiv: Mathematics::Metric Geometry, Mathematics::Differential Geometry
The isoperimetric inequality for Steiner symmetrization of any\ud codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.
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    • [1] L. Ambrosio, N. Fusco & D. Pallara. Functions of bounded variation and free discontinuity problems, in the Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York (2000).
    • [2] F.J. Almgren & E.H. Lieb. Symmetric rearrangement is sometimes continuous. J. Amer. Math. Soc. 2, 683- 773 (1989).
    • [3] A.Barvinok. A course in convexity, in the Graduate Studies in Mathematics, vol. 54. American Mathematical Society, Providence, 2002.
    • [4] F. Brock & A. Y. Solynin. An approach to symmetrization via polarization. Trans. Amer. Math. Soc. 352, 1759-1796 (2000).
    • [5] M. Chleb´ık, A. Cianchi & N. Fusco. The perimeter inequality under Steiner symmetrization: cases of equality. Ann. of Math. 162, 525-555 (2005).
    • [6] S.-K. Chua & R. L. Wheeden. Weighted Poincar´e inequalities on convex domains. Math. Res. Lett. 17, 993-1011 (2010).
    • [7] A. Cianchi & N. Fusco. Functions of bounded variation and rearrangements. Arch. for Rat. Mech. and Anal. 165, 1-40 (2002).
    • [8] M. Cicalese & G. Leonardi. A Selection Principle for the Sharp Quantitative Isoperimetric Inequality. Preprint (2010).
    • [9] I. Drelichman & R.G. Dur´an. Improved Poincar´e inequalities with weights. J. Math. Anal. Appl. 347, 286-293 (2008).
    • [10] L. Esposito, N. Fusco & C. Trombetti. A quantitative version of the isoperimetric inequality: the anisotropic case. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4, 619-651 (2005).
    • [11] A. Figalli, F. Maggi & A. Pratelli. A mass transportation approach to quantitative isoperimetric inequalities. Invent. Math. 182, 167-211 (2010).
    • [12] B. Fuglede. Stability in the isoperimetric problem for convex or nearly spherical domains in Rn. Trans. Amer. Math. Soc. 314, 619-638 (1989).
    • [13] N. Fusco, F. Maggi & A. Pratelli. The sharp quantitative isoperimetric inequality. Ann. of Math. 168, 941-980 (2008).
    • [14] R.R. Hall. A quantitative isoperimetric inequality in n-dimensional space. J. Reine Angew. Math. 428, 161- 176 (1992).
    • [15] R.R. Hall, W.K. Hayman & A.W. Weitsman. On asymmetry and capacity. J. d'Analyse Math. 56, 87-123 (1991).
    • [16] V.G. Maz'ja. Sobolev spaces, in the Springer Series in Soviet Mathematics. Springer-Verlag, Berlin (1985).
    • [17] A.I. Vol'pert. Spaces BV and quasi-linear equations. Math. USSR Sb. 17, 225-267 (1967). (M. Barchiesi) Dipartimento di Matematica ed Applicazioni, Universita` di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy E-mail address: (F. Cagnetti) Departamento de Matema´tica Instituto Superior T´ecnico, Av. Rovisco Pais, 1049- 001 Lisboa, Portugal E-mail address: (N. Fusco) Dipartimento di Matematica ed Applicazioni, Universita` di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy E-mail address:
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