Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces

Communications in Analysis and Geometry

Volumn 9, Issue 5, 2001, Pages 1093-1138

  Ritoré, Manuel ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041906588     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.2001.v9.n5.a5     Document Type: Article

References (24)

1. J.L. Barbosa, M. do Carmo and J. Eschenburg, Stability of hypersurfaces with constant mean curvature in Riemannian manifolds, Math. Z., 197 (1988), 123-138.
2. 2, Ann. Sci. École Norm. Sup., 19(4) (1986), 479-490.
3. I. Benjamini and J. Cao, A new isoperimetric comparison theorem for surfaces of varíable curvature, Duke Math. J., 85(2) (1996), 359-397.
4. I. Chavel, Eigenvalues in Riemannian Geometry, Pure and Applied Mathematics, 115, Academic Press, Inc., Orlando, Fla., 1984.
5. I. Chavel, Riemannian Geometry - a modern introduction, Cambridge Tracts in Mathematics, 108, Cambridge University Press, Cambridge, 1993.
6. C. Delaunay, Sur la surface de revolution dont la courbure moyenne est constante, J. Math. Pures Appl., 16 (1841), 309-321.
7. M. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Inc., 1976.
8. F. Fiala, Le problème des isopérimètres sur les surfaces ouvertes à courbure positive, Comment. Math. Helv., 13 (1941), 293-346.
9. M. Giaquinta and S. Hildebrandt, Calculus of Variations I: The Lagrangian formalism, Grundlehren Math. Wiss., 310, Springer Verlag, Berlin, 1996.
10. E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, 80, Birkhäuser, Verlag, Basel-Boston, 1984.
11. M. Grayson, Shortening embedded curves, Ann. of Math., 129(2) (1989), 71-111.
12. P. Hartman, Geodesic parallel coordinates in the large, Amer. J. Math., 8 (1964), 705-727.
13. P. Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964.
14. H. Howards, M. Hutchings and F. Morgan, The isoperimetric problem on surfaces, Amer. Math. Monthly, 106(5) (1999), 430-439.
15. H. Howards, M. Hutchings and F. Morgan, The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature, Trans. Amer. Math. Soc., 352(11) (2000), 4889-4909.
16. 2, Proc. Amer. Math. Soc., 32 (1972), 139-141.
17. S. Montiel, Unicity of constant mean curvature hypersurfaces in foliated Riemannian manifolds, Indiana Univ. Math. J., 48(2) (1999), 711-748.
18. R. Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. (N.S.), 84(6) (1978), 1182-1238.
19. R. Osserman, Bonnesen-style isoperimetric inequalities, Amer. Math. Monthly, 86(1) (1979), 1-29.
20. P. Pansu, Sur la régularité du profil isopérimétrique des surfaces riemannienes compactes, Ann. Inst. Fourier (Grenoble), 48(1) (1998), 247-264.
21. M. Ritoré, Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces: tori, Klein bottles and symmetric cylinders, in preparation.
22. E. Schmidt, Über eine neue Methode zur Behandlung einer Klasse isoperimetrischer Aufgaben im Grossen, Math. Z., 47 (1942), 489-642.
23. P. Topping, The isoperimetric inequality on a surface, Manuscripta Math., 100(1) (1999), 23-33.
24. R. Ye, Foliation by constant mean curvature spheres, Pacific J. Math., 147(2) (1991), 381-396.