Skip to main content
SpringerLink
Log in

A sharp four dimensional isoperimetric inequality

  • Published:
Commentarii Mathematici Helvetici

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  • [A]T. Aubin,Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geometry11 (1976), 573–598.

    MathSciNet  MATH  Google Scholar 

  • [B]M. Berger,Lectures on geodesics in Riemannian geometry, Tata Institute, Bombay, 1965.

    MATH  Google Scholar 

  • [B-R]E. F. Beckenbach andT. Radó,Subharmonic functions and surfaces of negative curvature, Trans. Amer. Math. Soc.35 (1933), 662–674.

    Article  MathSciNet  Google Scholar 

  • [B-C]R. Bishop andR. Crittenden,Geometry of manifolds, Academic Press, 1964.

  • [Bo]E. Bombieri,Theory of minimal surfaces, and a counterexample to the Bernstein conjecture in high dimension, Lecture Notes, Courant Inst., 1970.

  • [C]C. Croke,Some isoperimetric inequalities and eigenvalue estimates, Ann. Scient. Éc. Norm. Sup., 4e série t.13, 1980, 419–435.

    MathSciNet  MATH  Google Scholar 

  • [F-F]H. Federer andW. Flemming,Normal integral currents, Ann. of Math.72 (1960), 458–520.

    Article  MathSciNet  Google Scholar 

  • [H-S]D. Hoffman andJ. Spruck,Sobolev and isoperimetric inequalities for Riemannian submanifolds, Communications Pure Appl. Math.27 (1974), 715–727; correction, ibid. Communications Pure Appl. Math.28 (1975), 765–766.

    Article  MathSciNet  MATH  Google Scholar 

  • [Sa]L. A. Santaló,Integral geometry and geometric probability, (Encyclopedia of Mathematics and Its Applications), Addison-Wesley, London-Amsterdam-Don Mills, Ontario-Sydney-Tokyo, 1976.

    MATH  Google Scholar 

  • [Sc]E. Schmidt,Beweis der isoperimetrischen Eigenschaft der Kugel in hyperbolischen und spharischen Raum jeder Dimensionenzahl, Math. Z.49 (1943/44), 1–109.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Pennsylvania, 19104, Philadelphia, PA, USA

    Christopher B. Croke

Authors
  1. Christopher B. Croke
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by NSF Grant #MCS-01780

Rights and permissions

Reprints and permissions

About this article

Cite this article

Croke, C.B. A sharp four dimensional isoperimetric inequality. Commentarii Mathematici Helvetici 59, 187–192 (1984). https://doi.org/10.1007/BF02566344

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02566344

Keywords

Search

Navigation