Skip to main content
Log in

An isoperimetric comparison theorem

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [Alm] Almgren, F.: Optimal Isoperimetric Inequalities. Bull. Am. Math. Soc.13 (no. 2) (1985)

  • [Alm2] Almgren, F.: Optimal Isoperimetric Inequalities. Indiana Univ. Math. J.35 (no. 3) (1986)

  • [Aub] Aubin, T.: Problèmes isopérimétriques et espaces de sobolev. J. Differ. Geom.11, 573–598 (1976)

    Google Scholar 

  • [BGS] Ballmann, W., Gromov, M., Schroeder, V.: Manifolds of nonpositive curvature. Boston Basel Stuttgart: Birkhäuser 1985

    Google Scholar 

  • [BP] Bavard, C., Pansu, P.: Sur le volume minimal deR 2. Ann. Sci. Éc. Norm. Super., IV. Ser.19 (1986)

  • [BZ] Burago, Yu. D., Zalgaller, V.A.: Geometric Inequalities. Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  • [Cr1] Croke, C.: A sharp four dimensional isoperimetric inequality. Comment. Math. Helv.59, 187–192 (1984)

    Google Scholar 

  • [Cr2] Croke, C.: Some isoperimetric inequalities and eigenvalue estimates. Ann. Sci. Éc. Norm. Supér. IV. Ser.,13, 419–435 (1980)

    Google Scholar 

  • [Fed] Federer, H.: Geometric Measure Theory. Berlin Heidelberg New York: Springer 1969

    Google Scholar 

  • [Gall] Gallot, S.: Inegalitiés isopérimétriques et analytiques sur les variétés Riemanniennes. (Astérisque, vols. 163–164, pp. 31–91) Paris: Soc. Math. France 1988

    Google Scholar 

  • [GLP] Gromov, M., Lafontaine, J., Pansu, P.: Structures métriques pour les variétés Riemanniennes. Paris: Cedic/Fernand Nathan 1981

    Google Scholar 

  • [HS] Hoffman, D., Spruck, J.: Sobolev and isoperimetric inequalities for Riemannian submanifolds, Commun. Pure Appl. Math.27, 715–727 (1974)

    Google Scholar 

  • [SZ] Schroeder, V., Ziller, W.: Local rigidity of symmetric spaces. Trans. Am. Math. Soc.320 (no. 1) (1990)

    Google Scholar 

  • [Sim] Simon, L.: Lectures on Geometric Measure Theory. (Proc. Cent. Math. Anal., Aust. Natl. Univ. vol. 3) Canberra: Cent. Math. Anal. 1983

    Google Scholar 

  • [Weil] Weil, A.: Sur les surfaces a courbure negative. C.R. Acad. Sci., Paris182 1069–1071 (1926)

    Google Scholar 

  • [Whi] White, B.: Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds. J. Differ. Geom.33 (no. 2) 413–443 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Oblatum 13-II-1991 & 30-IX-1991

Supported by an NSF Postdoctoral Fellowship

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kleiner, B. An isoperimetric comparison theorem. Invent Math 108, 37–47 (1992). https://doi.org/10.1007/BF02100598

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02100598

Keywords

Navigation