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Volumn 11, Issue 3, 2001, Pages 509-517

The isoperimetric problem in complete surfaces of nonnegative curvature

Author keywords

Constant geodesic curvature; Isoperimetric domains; Isoperimetric inequality; Isoperimetric problem; Stability

Indexed keywords


EID: 0141793896     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02922017     Document Type: Article
Times cited : (27)

References (21)
  • 2
    • 0040151814 scopus 로고    scopus 로고
    • A new isoperimetric comparison theorem for surfaces of variable curvature
    • Benjamini, I. and Cao, J. A new isoperimetric comparison theorem for surfaces of variable curvature, Duke Math. J., 85(2), 359-397, (1996).
    • (1996) Duke Math. J. , vol.85 , Issue.2 , pp. 359-397
    • Benjamini, I.1    Cao, J.2
  • 3
    • 0002587690 scopus 로고
    • Kürzeste wege und totalkrümmung auf flächen
    • Cohn-Vossen, S. Kürzeste wege und totalkrümmung auf flächen, Comp. Math., 2, 69-133, (1935).
    • (1935) Comp. Math. , vol.2 , pp. 69-133
    • Cohn-Vossen, S.1
  • 4
    • 0000580123 scopus 로고
    • Le problème des isopérimètres sur les surfaces ouvertes à courbure positive
    • Fiala, F. Le problème des isopérimètres sur les surfaces ouvertes à courbure positive, Comment. Math. Helv., 13, 293-346, (1941).
    • (1941) Comment. Math. Helv. , vol.13 , pp. 293-346
    • Fiala, F.1
  • 5
    • 0003343498 scopus 로고
    • Minimal surfaces and functions of bounded variation
    • Birkhäuser Verlag, Basel-Boston
    • Giusti, E. Minimal surfaces and functions of bounded variation, Monographs in Mathematics, no. 80, Birkhäuser Verlag, Basel-Boston, 1984.
    • (1984) Monographs in Mathematics , vol.80
    • Giusti, E.1
  • 6
    • 0000003902 scopus 로고
    • Geodesic parallel coordinates in the large
    • Hartman, P. Geodesic parallel coordinates in the large, Am. J. Math., 8, 705-727, (1964).
    • (1964) Am. J. Math. , vol.8 , pp. 705-727
    • Hartman, P.1
  • 7
    • 0040647961 scopus 로고    scopus 로고
    • 3 of complete noncompact nonnegatively curved surfaces
    • 3 of complete noncompact nonnegatively curved surfaces, Manusc. Math., 94, 271-286, (1997).
    • (1997) Manusc. Math. , vol.94 , pp. 271-286
    • Hong, J.1
  • 8
    • 0033449295 scopus 로고    scopus 로고
    • The isoperimetric problem on surfaces
    • Howards, H., Hutchings, M., and Morgan, F. The isoperimetric problem on surfaces, Am. Math. Monthly, 106(5), 430-439, (1999).
    • (1999) Am. Math. Monthly , vol.106 , Issue.5 , pp. 430-439
    • Howards, H.1    Hutchings, M.2    Morgan, F.3
  • 9
    • 84972576734 scopus 로고
    • On soap bubbles and isoperimetric regions in noncompact symmetric spaces
    • Hsiang, W.-Y. On soap bubbles and isoperimetric regions in noncompact symmetric spaces, Tôhoku Math. J., 44(2), 151-175, (1992).
    • (1992) Tôhoku Math. J. , vol.44 , Issue.2 , pp. 151-175
    • Hsiang, W.-Y.1
  • 11
    • 23044524150 scopus 로고    scopus 로고
    • The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature
    • Morgan, F., Hutchings, M., and Howards, H. The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature, Trans. Am. Math. Soc., 352(11), 4889-4909, (2000).
    • (2000) Trans. Am. Math. Soc. , vol.352 , Issue.11 , pp. 4889-4909
    • Morgan, F.1    Hutchings, M.2    Howards, H.3
  • 12
    • 0001192899 scopus 로고    scopus 로고
    • Some sharp isoperimetric theorems for Riemannian manifolds
    • Morgan, F. and Johnson, D. Some sharp isoperimetric theorems for Riemannian manifolds, Indiana Univ. Math. J., 49(3), 1017-1041, (2000).
    • (2000) Indiana Univ. Math. J. , vol.49 , Issue.3 , pp. 1017-1041
    • Morgan, F.1    Johnson, D.2
  • 13
    • 0000190919 scopus 로고
    • The isoperimetric inequality
    • N.S.
    • Osserman, R. The isoperimetric inequality, Bull. Am. Math. Soc., (N.S.), 84(6), 1182-1238, (1978).
    • (1978) Bull. Am. Math. Soc. , vol.84 , Issue.6 , pp. 1182-1238
    • Osserman, R.1
  • 14
    • 0039756621 scopus 로고    scopus 로고
    • Sur la régularité du profil isopérimétrique des surfaces riemannienes compactes
    • Grenoble
    • Pansu, P. Sur la régularité du profil isopérimétrique des surfaces riemannienes compactes, Ann. Inst. Fourier, (Grenoble), 48(1), 247-264, (1998).
    • (1998) Ann. Inst. Fourier , vol.48 , Issue.1 , pp. 247-264
    • Pansu, P.1
  • 15
    • 0041906588 scopus 로고    scopus 로고
    • Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces
    • to appear
    • Ritoré, M. Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces, Comm. Anal. Geom., to appear.
    • Comm. Anal. Geom.
    • Ritoré, M.1
  • 16
    • 0003346020 scopus 로고
    • Convex Analysis
    • Princeton University Press, Princeton, NJ
    • Rockafellar, R.T. Convex Analysis, Princeton Mathematical Series, no. 28, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Princeton Mathematical Series , vol.28
    • Rockafellar, R.T.1
  • 17
    • 0042297449 scopus 로고
    • Über eine neue methode zur behandlung einer klasse isoperimetrischer aufgaben im grossen
    • Schmidt, E. Über eine neue methode zur behandlung einer klasse isoperimetrischer aufgaben im grossen, Math. Z., 47, 489-642, (1942).
    • (1942) Math. Z. , vol.47 , pp. 489-642
    • Schmidt, E.1
  • 18
    • 11244285389 scopus 로고
    • The length function of geodesic parallel circles
    • Tokyo
    • Shiohama, K. and Tanaka, M. The length function of geodesic parallel circles, Adv. Studies in Pure Math., 22, 299-308, Tokyo, (1993).
    • (1993) Adv. Studies in Pure Math. , vol.22 , pp. 299-308
    • Shiohama, K.1    Tanaka, M.2
  • 19
    • 22844453397 scopus 로고    scopus 로고
    • The isoperimetric inequality on a surface
    • Topping, P. The isoperimetric inequality on a surface, Manusc. Math., 100, 23-33, (1999).
    • (1999) Manusc. Math. , vol.100 , pp. 23-33
    • Topping, P.1
  • 20
    • 84972541930 scopus 로고
    • Complete surfaces of finite total curvature
    • White, B. Complete surfaces of finite total curvature, J. Differential Geom., 26, 315-326, (1987).
    • (1987) J. Differential Geom. , vol.26 , pp. 315-326
    • White, B.1
  • 21
    • 0010675442 scopus 로고
    • Distance nonincreasing retraction on a complete open manifold of nonnegative sectional curvature
    • Yim, J.-W. Distance nonincreasing retraction on a complete open manifold of nonnegative sectional curvature, Ann. Global Anal. Geom., 6(2), 191-206, (1988).
    • (1988) Ann. Global Anal. Geom. , vol.6 , Issue.2 , pp. 191-206
    • Yim, J.-W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.