Geodesic
The Isoperimetric Inequality for Curves with Self-Intersections
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 161-167

Voir la notice de l'article provenant de la source Cambridge University Press

Banchoff and Pohl [3] have proved the following generalization of the isoperimetric inequality. Theorem. If γ is a closed, not necessarily simple, planar curve of length L, and w(p) is the winding number of a variable point p with respect to γ, then 1 with equality holding if and only if γ is a circle traversed a finite number of times in the same sense. 
Vogt, Andrew. The Isoperimetric Inequality for Curves with Self-Intersections. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 161-167. doi: 10.4153/CMB-1981-026-8
@article{10_4153_CMB_1981_026_8,
     author = {Vogt, Andrew},
     title = {The {Isoperimetric} {Inequality} for {Curves} with {Self-Intersections}},
     journal = {Canadian mathematical bulletin},
     pages = {161--167},
     year = {1981},
     volume = {24},
     number = {2},
     doi = {10.4153/CMB-1981-026-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-026-8/}
}
TY  - JOUR
AU  - Vogt, Andrew
TI  - The Isoperimetric Inequality for Curves with Self-Intersections
JO  - Canadian mathematical bulletin
PY  - 1981
SP  - 161
EP  - 167
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-026-8/
DO  - 10.4153/CMB-1981-026-8
ID  - 10_4153_CMB_1981_026_8
ER  - 
%0 Journal Article
%A Vogt, Andrew
%T The Isoperimetric Inequality for Curves with Self-Intersections
%J Canadian mathematical bulletin
%D 1981
%P 161-167
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-026-8/
%R 10.4153/CMB-1981-026-8
%F 10_4153_CMB_1981_026_8

[1] 1. Aleksandrov, P. S., Combinatorial Topology, vol. 1, Graylock Press, Rochester, N.Y., 1956 (translation by Horace Komm). Google Scholar

[2] 2. Apostol, T. M., Mathematical Analysis, Addison-Wesley, Reading, Mass., 1957. Google Scholar

[3] 3. Banchoff, T. F. and Pohl, W. F., A generalization of the isoperimetric inequality, J. Differential Geometry. 6 (1971), 175-192. Google Scholar

[4] 4. Courant, R. and Hilbert, D., Methods of Mathematical Physics, vol. 1, Interscience Publishers, Inc., New York, 1953. Google Scholar

[5] 5. Fédérer, H., Geometric Measure Theory, Springer-Verlag, Berlin, 1969. Google Scholar

[6] 6. Hewitt, E. and Stromberg, K., Real and Abstract Analysis, Springer-Verlag, New York, 1965. Google Scholar

[7] 7. Newman, M. H. A., Elements of the Topology of Plane Sets of Points, University Press, Cambridge, England, 1964. Google Scholar

[8] 8. Osserman, R., The isoperimetric inequality, Bull. Amer. Math. Soc. 84. 6 (1978), 1182-1238. Google Scholar

[9] 9. RadÓ, T., A lemma on the topological index, Fund. Math.. 27 (1936), 212-225. Google Scholar

[10] 10. RadÓ, T., The isoperimetric inequality and the Lebesgue definition of surface area, Trans. Amer. Math. Soc.. 41 (1947), 530-555. Google Scholar

Cité par Sources :