Skip to main content
SpringerLink
Log in

Die symmetrische Kugelzone als extremaler Rotationskörper

  • Kurze Mitteilungen
  • Published:
Experientia Aims and scope Submit manuscript

Summary

For a convex body in three dimensions letV be the volume,F the surface area, andM the total mean curvature.

TheBrunn-Minkowski theory gives the following well-known result: Among all the convex bodies withV andF fixed the spherical cap-body gives the maximum ofM.—The question regarding the minimum ofM has not yet been solved for the general case.—The authors prove that the minimum ofM is given by the symmetrical spherical zone, if we restrict our investigation to bodies of revolution.

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

Literatur

  1. H. Brunn,Über Ovale und Eiflächen (Diss. München, 1887).

    Google Scholar 

  2. H. Minkowski, Math. Ann.57, 447 (1903); Ges. Abh. Bd. 2, 230–276;Theorie der konvexen Körper, insbesondere Begründung ihres Oberflächenbegriffs, Ges. Abh. Bd. 2, 131–229.

    Article  Google Scholar 

  3. W. Blaschke, Jber. Dtsch. Math. Ver.25, 125 (1917.)

    Google Scholar 

  4. H. Hadwiger, El. Math.2, 51 (1947).

    Google Scholar 

  5. T. Bonnesen undW. Fenchel, Ergebn. Math.3, 84 (1934).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Seminar der Universität Bern, Switzerland

    H. Hadwiger, P. Glur & H. Bieri

Authors
  1. H. Hadwiger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Glur
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Bieri
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hadwiger, H., Glur, P. & Bieri, H. Die symmetrische Kugelzone als extremaler Rotationskörper. Experientia 4, 304–305 (1948). https://doi.org/10.1007/BF02164459

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02164459

Search

Navigation