New extremal problems for the Riemannian recognition program via Alexandrov geometry
Tóm tắt
Từ khóa
Tài liệu tham khảo
Abresch, Uwe, 1990, On complete manifolds with nonnegative Ricci curvature, J. Amer. Math. Soc., 3, 355, 10.2307/1990957
Berestovskiĭ, V. N., 1986, Spaces with bounded curvature and distance geometry, Sibirsk. Mat. Zh., 27, 11
Burago, Yu., 1992, A. D. Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk, 47, 3, 10.1070/RM1992v047n02ABEH000877
Cheeger, Jeff, 1975, Comparison theorems in Riemannian geometry
Coxeter, H. S. M., 1961, Introduction to geometry
Fáry, István, 1949, Sur la courbure totale d’une courbe gauche faisant un nœud, Bull. Soc. Math. France, 77, 128, 10.24033/bsmf.1405
Gromoll, Detlef, 1987, A generalization of Berger’s rigidity theorem for positively curved manifolds, Ann. Sci. \'{E}cole Norm. Sup. (4), 20, 227, 10.24033/asens.1530
Gromov, Mikhael, 1981, Groups of polynomial growth and expanding maps, Inst. Hautes \'{E}tudes Sci. Publ. Math., 53, 10.1007/BF02698687
Gromov, Mikhael, 1983, Filling Riemannian manifolds, J. Differential Geom., 18, 1
Grove, Karsten, 1991, Metric and topological measurements of manifolds, 511
Grove, Karsten, 1992, Curvature, triameter, and beyond, Bull. Amer. Math. Soc. (N.S.), 27, 261, 10.1090/S0273-0979-1992-00308-7
Grove, Karsten, 1988, Bounding homotopy types by geometry, Ann. of Math. (2), 128, 195, 10.2307/1971439
Grove, Karsten, 1988, Homotopy types of positively curved manifolds with large volume, Amer. J. Math., 110, 1183, 10.2307/2374690
Grove, Karsten, 1991, Manifolds near the boundary of existence, J. Differential Geom., 33, 379
Grove, Karsten, 1990, A pinching theorem for homotopy spheres, J. Amer. Math. Soc., 3, 671, 10.2307/1990933
Grove, Karsten, 1990, Geometric finiteness theorems via controlled topology, Invent. Math., 99, 205, 10.1007/BF01234418
Grove, Karsten, 1995, Hard and soft packing radius theorems, Ann. of Math. (2), 142, 213, 10.2307/2118635
Hamilton, Richard S., 1982, Three-manifolds with positive Ricci curvature, J. Differential Geometry, 17, 255
Hsiang, Wu-Yi, 1989, On the topology of positively curved 4-manifolds with symmetry, J. Differential Geom., 29, 615
F. Nielsen, On the sum of distances between 𝑛 points on a sphere, Nordisk Mat. Tidsskr. 13 (1965), 45-50. (Danish)
Otsu, Yukio, 1989, A new version of differentiable sphere theorem, Invent. Math., 98, 219, 10.1007/BF01388850
G. Perelman, Alexandrov’s spaces with curvatures bounded from below II, preprint.
Petersen, Peter, V, 1990, A finiteness theorem for metric spaces, J. Differential Geom., 31, 387
Petersen, Peter, V, 1993, Gromov-Hausdorff convergence of metric spaces, 489, 10.1016/j.jpaa.2011.12.018
Plaut, Conrad, 1996, Spaces of Wald curvature bounded below, J. Geom. Anal., 6, 113, 10.1007/BF02921569