Minimizing currents in open manifolds and the n - 1 homology of nonnegatively Ricci curved manifolds

American Journal of Mathematics

Volumn 121, Issue 6, 1999, Pages 1253-1278

  Itokawa, Yoe ^a   Kobayashi, Ryoichi ^b  

^a FUKUOKA INSTITUTE OF TECHNOLOGY   (Japan)

^b NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033475144     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.1999.0039     Document Type: Article

References (23)

1. U. Abresch and D. Gromoll, On complete manifolds with nonnegative Ricci curvature, J. Amer. Math. Soc. 3 (1990), 355-374.
2. F. J. Almgren Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc. 165 (1976).
3. R. Bishop and R. Crittenden, Geometry of Manifolds, Academic Press, New York, 1965.
4. J. Cheeger and T. Colding, Almost rigidity of warped products and the structure of spaces with curvature bounded below, preprint.
5. J. Cheeger and D. Gromoll, The splitting theorem for manifolds of non-negative Ricci curvature, J. Differential Geom. 6 (1971), 119-128.
6. J. Cheeger, M. Gromov, and M. Taylor, Finite propagation speed, kernel estimate for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1974), 15-53.
7. M. Gromov, Paul Levy's isoperimetric inequality, IHES preprint, 1980.
8. P. Hartman, Oscillation criteria for self-adjoint second-order differential systems and "principal sectional curvatures," J. Differential Equations 34 (1979), 326-337.
9. E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. École Norm. Sup. (4) 11 (1978), 451-470.
10. D. Hoffman and J. Spruck, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math. 27 (1974), 715-727; Corrections, Comm. Pure Appl. Math. 28 (1975), 765-766.
11. D. Hoffman and J. Spruck, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math. 27 (1974), 715-727; Corrections, Comm. Pure Appl. Math. 28 (1975), 765-766.
12. Y. Itokawa, On minimal hypersurfaces of nonnegatively Ricci curved manifolds, Internat. J. Math. Math. Sci. 16 (1993), 573-578.
13. Y. Itokawa and R. Kobayashi, Geometric measure theory and manifolds of nonnegative Ricci curvature, Proc. Japan Acad. Ser. A Math. Sci. 72 (1996), 128-130.
14. Y. Itokawa and K. Shiohama, The unboundedness of certain minimal submanifolds of positively curved Riemannian spaces, preprint.
15. A. Kasue, Ricci curvature, geodesics, and some geometric properties of Riemannian manifolds with boundary, J. Math. Soc. Japan 35 (1983), 117-131.
16. H. B. Lawson, Minimal Varieties in Real and Complex Geometry, Les Presses de l'Université de Montréal, Montreal, 1974.
17. D. Meyer, Sur les hypersurface minimales des variétés riemannienne à curbure de Ricci positive ou nulle, Bull. Soc. Math. France 111 (1983), 359-366.
18. G. Perelman, Manifolds of positive Ricci curvature with almost maximal volume, J. Amer. Math. Soc. 7 (1994), 299-305.
19. J. Pitts, Existence and Regularity of Minimal Surfaces on Riemannian Manifolds, Princeton University Press, Princeton, 1981.
20. Z. Shen, On complete manifolds of nonnegative kth-Ricci curvature, Trans. Amer. Math. Soc. 338 (1993), 289-310.
21. Z. Shen and G. Wei, Volume growth and finite topological type, Proc. Sympos. Pure Math., vol. 54, Amer. Math. Soc., Providence, RI, 1993, pp. 539-549.
22. L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Center for Mathematical Analysis, Australian National University, vol. 3, Center for Mathematical Analysis, Australian National University, Australia, 1983.
23. S. T. Yau, Some function-theoretic properties of complete manifolds and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 659-670.