Generalized degree and optimal loewner-type inequalities

Israel Journal of Mathematics

Volumn 141, Issue , 2004, Pages 221-233

  Ivanov, Sergei V ^a   Katz, Mikhail G ^b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042528460     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02772220     Document Type: Article

References (24)

1. [BaK98] I. Babenko and M. Katz, Systolic freedom of orientable manifolds, Annales Scientifiques de l'École Normale Supérieure (Paris) 31 (1998), 787-809.
2. [BCIK] V. Bangert, C. Croke, S. Ivanov and M. Katz, Boundary case of equality in optimal Loewner-type inequalities and the filling area conjecture, in preparation.
3. A] V. Bangert and M. Katz, Stable systolic inequalities and cohomology products, Communications on Pure and Applied Mathematics 56 (2003), 979-997.
4. B] V. Bangert and M. Katz, An optimal Loewner-type systolic inequality and harmonic one-forms of constant norm, arXiv:math.DG/0304494.
5. [Bar57] E. S. Barnes, On a theorem of Voronoi, Proceedings of the Cambridge Philosophical Society 53 (1957), 537-539.
6. [BI94] D. Burago and S. Ivanov, Riemannian tori without conjugate points are flat, Geometric and Functional Analysis 4 (1994), 259-269.
7. [BI95] D. Burago and S. Ivanov, On asymptotic volume of tori, Geometric and Functional Analysis 5 (1995), 800-808.
8. [Ch93] I. Chavel, Riemannian Geometry - A Modern Introduction, Cambridge Tracts in Mathematics, 108,Cambridge University Press, Cambridge, 1993.
9. [CK03] C. Croke and M. Katz, Universal volume bounds in Riemannian manifolds, Surveys in Differential Geometry 8, Lectures on Geometry and Topology held in honor of Calabi, Lawson, Siu, and Uhlenbeck at Harvard University, May 3-5, 2002 (S. T. Yau, ed.), International Press, Somerville, MA, 2003, pp. 109-137.
10. [FK92] H. M. Farkas and I. Kra, Riemann Surfaces, Second edition, Graduate Texts in Mathematics 71, Springer-Verlag, New York, 1992.
11. [Fe69] H. Federer, Geometric Measure Theory, Springer, Berlin, 1969.
12. [Gr81] M. Gromov, Structures métriques pour les variétés riemanniennes (J. Lafontaine and P. Pansu, eds.), Textes Mathématiques, 1, CEDIC, Paris, 1981.
13. [Gr83] M. Gromov, Filling Riemannian manifolds, Journal of Differential Geometry 18 (1983), 1-147.
14. [Gr96] M. Gromov, Systoles and intersystolic inequalities, in Actes de la Table Ronde de Géométrie Différentielle (Luminy, 1992), Séminaires et Congrès, Vol. 1, Société Mathématique de France, Paris, 1996, pp. 291-362.
15. [Gr99] M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, Vol. 152, Birkháuser, Boston, 1999.
16. [Iv02] S. Ivanov, On two-dimensional minimal fillings, St. Petersburg Mathematical Journal 13 (2002), 17-25.
17. [Ka03] M. Katz, Four-manifold systoles and surjectivity of period map, Commentarii Mathematici Helvetici 78 (2003), 772-876.
18. [KKS] M. Katz, M. Kreck and A. Suciu, Free abelian covers, short loops, stable length, and systolic inequalities
19. [LLS90] J. C. Lagarias, H. W. Lenstra Jr. and C. P. Schnorr, Bounds for Korkin-Zolotarev reduced bases and successive minima of a lattice and its reciprocal lattice, Combinatorica 10 (1990), 343-358.
20. [Li69] A. Lichnerowicz, Applications harmoniques dans un tore, Comptes Rendus de l'Académie des Sciences, Paris, Série I 260 (1969), 912-916.
21. [MS86] V. D. Milman and G. Schechtman, Asymptotic theory of finite-dimensional normed spaces (with an appendix by M. Gromov), Lecture Notes in Mathematics 1200, Springer-Verlag, Berlin, 1986.
22. [NR02] A. Nabutovsky and R. Rotman, The length of the shortest closed geodesic on a 2-dimansional sphere, International Mathematics Research Notices 2002:23 (2002), 1211-1222.
23. [Pu52] P. M. Pu, Some inequalities in certain nonorientable Riemannian manifolds, Pacific Journal of Mathematics 2 (1952), 55-71.
24. [Sa04] S. Sabourau, Filling radius and short closed geodesics of the two-sphere, Bulletin de la Société Mathématique de France, to appear.