Löwner's conjecture, the Besicovitch barrel, and relative systolic geometry
Sbornik. Mathematics, Tome 193 (2002) no. 4, pp. 473-486 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to relative systolic geometry on a compact manifold with boundary. Sufficient conditions ensuring the intersystolic rigidity or intersystolic softness of such manifolds are analyzed. Several open questions are formulated.
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I. K. Babenko. Löwner's conjecture, the Besicovitch barrel, and relative systolic geometry. Sbornik. Mathematics, Tome 193 (2002) no. 4, pp. 473-486. http://geodesic.mathdoc.fr/item/SM_2002_193_4_a0/

[1] Berger M., “A l'ombre de Löwner”, Ann. Sci. École Norm. Sup. (4), 5 (1972), 241–260 | MR | Zbl

[2] Berger M., “Systoles et applications selon Gromov”, Séminaire Bourbaki. 1992/93, Exposé 771, Astérisque, 216, Soc. Math. France, Paris, 1993, 279–310 | MR | Zbl

[3] Burago Yu., Zalgaller V., Geometricheskie neravenstva, Nauka, M., 1980 | MR | Zbl

[4] Besicovitch A. S., “On two problems of Löwner”, J. London Math. Soc., 27:2 (1952), 141–144 | DOI | MR | Zbl

[5] Almgren F., “An isoperimetric inequality”, Proc. Amer. Math. Soc., 15:2 (1964), 284–285 | DOI | MR | Zbl

[6] Derrick W. R., “A weighted volume-diameter inequality for $n$-cubes”, J. Math. Mech., 18:5 (1969), 453–472 | MR | Zbl

[7] Derrick W. R., “A volume-diameter inequality for $n$-cubes”, J. Anal. Math., 22 (1969), 1–36 | DOI | MR | Zbl

[8] Gromov M., “Filling Riemannian manifolds”, J. Differential Geom., 18:1 (1983), 1–147 | MR | Zbl

[9] Babenko I., Forte souplesse intersystolique de variétés ferméis et de phat{o}lyhédres, Université Montpellier-II prépublication, No 13, 2000

[10] Gromov M., Metric structures for Riemannian and non-Riemannian spaces, Progr. Math., 152, Birckhäuser, Boston, 1999 | MR | Zbl

[11] Hebda D., “The collars of Riemannian manifolds and stable isosystolic inequalities”, Pacific J. Math., 121:2 (1986), 339–356 | MR | Zbl

[12] Bangert V., Katz M., Mass inequalities associated to cohomology products, Preprint, 2001 | MR | Zbl

[13] Vershinin V., Cobordisms and spectral sequences, Trans. Math. Monogr., 130, Amer. Math. Soc., Providence, RI, 1993 | MR | Zbl

[14] Federer H., Geometric mesure theory, Springer-Verlag, Berlin, 1969 | MR

[15] Federer H., “Real flat chains, cochains and variational problems”, Indiana Univ. Math. J., 24 (1974), 351–407 | DOI | MR | Zbl

[16] Babenko I., Katz M., “Systolic freedom of orientable manifolds”, Ann. Sci. École Norm. Sup. (4), 31:6 (1998), 787–809 | MR | Zbl

[17] Katz M., Appendix D in [10]