Quantitative isoperimetric inequalities for a class of nonconvex sets

  • Giovanni ColomboEmail author
  • Khai T. Nguyen


Quantitative versions (i.e., taking into account a suitable “distance” of a set from being a sphere) of the isoperimetric inequality are obtained, in the spirit of Fuglede (Trans Am Math Soc 314:619–638, 1989) and Fusco et al. (Ann Math 168:941–980, 2008) for a class of not necessarily convex sets called φ-convex sets. Our work is based on geometrical results on φ-convex sets, obtained using methods of both nonsmooth analysis and geometric measure theory.


Sets with positive reach External sphere condition Internal cone condition Isoperimetric deficiency Spherical deviation Fraenkel asymmetry 

Mathematics Subject Classification (2000)

49J52 49Q05 26B30 49Q15 51M04 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Dipartimento di Matematica Pura e ApplicataUniversità di PadovaPadovaItaly

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