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On the isoperimetric deficit upper limit

Lei Ma|Jiazu Zhou|Wenxue Xu
대한수학회 (The Korean Mathematical Society)|2013.01|대한수학회보 (Bulletin of the KMS)|제50권 제1호|pp. 175-184

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참고문헌

키워드

convex domainthe Minkowski mixed areathe isoperimetric deficit upper limitthe Bonnesen style inequalitythe reverse Bonnesen style inequality
주제분류수학

초록

In this paper, the reverse Bonnesen style inequalities for con- vex domain in the Euclidean plane R2 are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geo- metric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style in- equalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).

Abstract

In this paper, the reverse Bonnesen style inequalities for con- vex domain in the Euclidean plane R2 are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geo- metric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style in- equalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).

참고문헌 (39)

  1. T. F. Banchoff, "A generalization of the isoperimetric inequality", J. Differential Geometry, 6, pp.175~192 (1974)
  2. J. Bokowski, "Integral representation of quermassintegrals and Bonnesenstyle inequalities", Arch. Math, 47(1), pp.79~89 (1986)
  3. T. Bonnesen, "Les probl´ems des isop´erim´etres et des is´epiphanes" (1929), Gauthier-Villars
  4. T. Bonnesen, "Theorie der konvexen K¨oeper, 2nd ed." (1974)
  5. O. Bottema, "Eine obere Grenze f¨ur das isoperimetrische Defizit ebener Kurven", Nederl. Akad. Wetensch. Proc, 66, pp.442~446 (1933)
  6. Yu. D. Burago, "Geometric Inequalities" (1988), Springer
  7. V. Diskant, "A generalization of Bonnesen’s inequalities", Soviet Math. Dokl, 14, pp.1728~1731 (1973)
  8. H. Flanders, "A proof of Minkowski’s inequality for convex curves", Amer. Math. Monthly, 75, pp.581~593 (1968)
  9. E. Grinberg, "Integral Geometry and Convexity", Proceed- ings of the International Conference (2006)
  10. E. Grinberg, "The symetric isoperimetric deficit and the containment problem in a plan of constant curvature", ~
  11. L. Gysin, "The isoperimetric inequality for nonsimple closed curves", Proc. Amer. Math. Soc, 118(1), pp.197~203 (1993)
  12. H. Hadwiger, "Die isoperimetrische Ungleichung in Raum", Elemente der Math, 3, pp.25~38 (1948)
  13. H. Hadwiger, "Vorlesungen ¨uber Inhalt, Oberfl¨ache und Isoperimetrie" (1957), Springer
  14. G. Hardy, "Inequalities" (1952), Cambradge Univ. Press
  15. R. Howard, "The sharp Sobolev inequality and the Banchoff-Pohl inequality on surfaces", Proc. Amer. Math. Soc, 126(9), pp.2779~2787 (1998)
  16. W. Y. Hsiang, "An elementary proof of the isoperimetric problem", Chinese Ann. Math. Ser. A, 23(1), pp.7~12 (2002)
  17. C. C. Hsiung, "Isoperimetric inequalities for two-dimensional Riemannian manifolds with boundary", Ann. of Math, 73(2), pp.213~220 (1961)
  18. H. Ku, "Isoperimetric inequalities on surfaces of constant curvature", Canad. J. Math, 49(6), pp.1162~1187 (1997)
  19. M. Li, "An upper limit for the isoperimetric deficit of convex set in a plane of constant curvature", Sci. in China, 53(8), pp.1941~1946 (2010)
  20. R. Osserman, "The isoperimetric inequality", Bull. Amer. Math. Soc, 84(6), pp.1182~1238 (1978)
  21. R. Osserman, "Bonnesen-style isoperimetric inequality", Amer. Math. Monthly, 86(1), pp.1~29 (1979)
  22. A. Pleijel, "On konvexa kurvor", Nordisk Math. Tidskr, 3, pp.57~64 (1955)
  23. G. Polya, "Isoperimetric inequalities in mathematical physics, Annals of Mathematics Studies, no. 27" (1951), Princeton University Press
  24. D. Ren, "Topics in Integral Geometry" (1994), World Scientific
  25. L. A. Santal´o, "Integral Geometry and Geometric Probability" (1976), Addison- Wesley
  26. R. Schneider, "Convex Bodies: The Brunn-Minkowski Theory" (1993), Cambridge Univ. Press
  27. E. Teufel, "A generalization of the isoperimetric inequality in the hyperbolic plane", Arch. Math, 57(5), pp.508~513 (1991)
  28. E. Teufel, "Isoperimetric inequalities for closed curves in spaces of constant curvature", Results Math, 22(1), pp.622~630 (1992)
  29. J. L. Weiner, "A generalization of the isoperimetric inequality on the 2-sphere", Indiana Univ. Math. J, 24, pp.243~248 (1974)
  30. J. L. Weiner, "Isoperimetric inequalities for immersed closed spherical curves", Proc. Amer. Math. Soc, 120(2), pp.501~506 (1994)
  31. S. T. Yau, "Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold", Ann. Sci. Ec. Norm. Super, 8(4), pp.487~507 (1975)
  32. G. Zhang, "Containment measures in integral geometry, Integral geometry and convexity", pp.153~168 (2006), World Sci. Publ.
  33. J. Zhou, "On Bonnesen-type inequalities", Acta. Math. Sinica, Chinese Series, 50(6), pp.1397~1402 (2007)
  34. Jiazu Zhou, "The Bonnesen-type inequalities in a plane of constant curvature", 대한수학회지, 44(6), pp.1363~1372 (2007), 대한수학회
  35. J. Zhou, "Some Bonnesen-style inequalities for higher dimensions", Acta. Math. Sinica
  36. J. Zhou, "The discrete isoperimetric deficit upper bound", ~
  37. J. Zhou, "Geometric inequalities from the viewpoint of integral geometry", Acta Math. Sci. Ser. A Chin. Ed, 30(5), pp.1322~1339 (2010)
  38. Jiazu Zhou, "SOME NEW BONNESEN-STYLE INEQUALITIES", 대한수학회지, 48(2), pp.421~430 (2011), 대한수학회
  39. C. Zeng, "The symmetric mixed isoperimetric inequality of two planar convex domains", Acta Math. Sinica, 55(3), pp.355~362 (2012)

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