The asymptotic cones of manifolds of roughly nonnegative radial curvature

 Mashiko Yukihiro MASHIKO Yukihiro
 Department Mathematics Faculty of Science and Engineering Saga University

 Nagano Koichi NAGANO Koichi
 Mathematical Institute Tohoku University

 Otsuka Kazuo OTSUKA Kazuo
 Graduate School of Mathematics Kyushu University
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Author(s)

 Mashiko Yukihiro MASHIKO Yukihiro
 Department Mathematics Faculty of Science and Engineering Saga University

 Nagano Koichi NAGANO Koichi
 Mathematical Institute Tohoku University

 Otsuka Kazuo OTSUKA Kazuo
 Graduate School of Mathematics Kyushu University
Abstract
We prove that the asymptotic cone of every complete, connected, noncompact Riemannian manifold of roughly nonnegative radial curvature exists, and it is isometric to the Euclidean cone over their Tits ideal boundaries.
Journal

 Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 57(1), 5568, 20050101
The Mathematical Society of Japan
References: 32

1
 Lower curvature bounds, Toponogov's theorem and bounded topology I

ABRESCH U.
Ann. Sci. Ecole Norm. Sup. 28, 651670, 1985
Cited by (1)

2
 Generalized Riemannian spaces

ALEXANDROV A. D.
Uspekhi Mat. Nauk 41(3), 344, 1986
Cited by (1)

3
 <no title>

ALEXANDROV A. D.
Intrinsic geometry of surfaces, 1967
Cited by (1)

4
 <no title>

BALLMANN W.
Lectures on spaces of nonpositive curvature, 1995
Cited by (1)

5
 <no title>

BALLMANN W.
Manifolds of nonpositive curvature, 1985
Cited by (1)

6
 <no title>

BURAGO D.
A course in metric geometry, 2001
Cited by (1)

7
 Critical points of distance of functions and applications to geometry

CHEEGER J.
Geometric topology : recent developments, (Montecatini Terme, 1990), 1991
Cited by (1)

8
 <no title>

GROMOV M.
Structures metriques pour les varietes riemanniennes, 1981
Cited by (1)

9
 <no title>

GROMOV M.
Metric structures for Riemannian and nonRiemannian spaces, 1998
Cited by (1)

10
 Maximal diameter theorems for manifolds with restricted radial curvature

ITOKAWA Y.
Proceedings of the Fifth Pacific Rim Geometry Conference, Sendai, 2000, 2001
Cited by (1)

11
 Generalized Toponogov's Theorem for manifolds with radial curvature bounded below

ITOKAWA Y.
Exploration in complex and Riemannian geometry, a volume dedicated to Robert E. Greene, 2003
Cited by (1)

12
 A compactification of a manifolds with asymptotically nonnegative curvature

KASUE A.
Ann. Sci. Ecole Norm. Sup. 21(4), 593622, 1988
Cited by (1)

13
 Complete open manifolds of nonnegative radial curvature

MACHIGASHIRA Y.
Pacific J. Math 165(1), 153160, 1994
Cited by (1)

14
 <no title>

MACHIGASHIRA Y.
Manifolds of roughly nonnegative radial curvature, 2001
Cited by (1)

15
 <no title>

NAGANO K.
The asymptotic cones of manifolds with asymptotically nonnegative curvature, 2001
Cited by (1)

16
 Asymptotic flatness and cone structure at infinity

PETRUNIN A.
Math. Ann. 321(4), 775788, 2001
Cited by (1)

17
 <no title>

SHIOHAMA K.
The geometry of total curvature on complete open surfaces, 2003
Cited by (1)

18
 A convergence theorem in the geometry of Alexandrov space

YAMAGUCHI T.
Actes de la Table Ronde de Geometrie Differentielle, Luminy, 1992, Semin. Congr., 1996
Cited by (1)

19
 Isometry groups of spaces with curvature bounded above

YAMAGUCHI T.
Math. Z. 232(2), 275286, 1999
Cited by (1)

20
 Manifolds of negative curvature

BISHOP R. L.
Trans. Amer. Math. Soc. 145, 149, 1969
DOI Cited by (7)

21
 A. D. Alexandrov spaces with curvatures bounded below

BURAGO Y.
Uspekhi Mat. Nauk 47(2), 351,222, 1992
DOI Cited by (7)

22
 Asymptotically flat manifolds of nonnegative curvature

DREES G.
Differential Geom. Appl. 4, 7790, 1994
DOI Cited by (1)

23
 Curvature, diameter and Betti numbers

GROMOV M.
Comment. Math. Helv. 56(2), 179195, 1981
DOI Cited by (4)

24
 Restrictions on the geometry at infinity of nonnegatively curved manifolds

GUIJARRO L.
Duke Math. J. 78(2), 257276, 1995
DOI Cited by (1)

25
 Manifolds with quadratic curvature decay and slow volume growth

LOTT J.
Ann. Sci. Ecole Norm. Sup. 33(4), 275290, 2000
DOI Cited by (1)

26
 Riemannian manifolds with positive radial curvature

MACHIGASHIRA Yoshiroh , SHIOHAMA Katsuhiro
Japanese journal of mathematics. New series 19(2), 419430, 19931201
JSTAGE References (19) Cited by (1)

27
 Manifolds with minimal radial curvature bounded from below and big radius

MARENICH V. B.
Indiana Univ. Math. J. 48(1), 249274, 1999
DOI Cited by (1)

28
 Mass of rays in Alexandrov spaces of nonnegative curvature

SHIOYA T.
Comment. Math. Helv. 69(2), 208228, 1994
DOI Cited by (3)

29
 Complete Kahler manifolds with nonpositive curvature of faster than quadratic decay

SIU Y. T.
Ann. of Math. (2) 105(2), 225264, 1977
DOI Cited by (1)

30
 A volume comparison theorem for manifolds with asymptotically nonnegative curvature and its applications

ZHU S. H.
Amer. J. Math. 116, 669682, 1994
DOI Cited by (1)

31
 THE IDEAL BOUNDARIES OF COMPLETE OPEN SURFACES

SHIOYA TAKASHI
Tohoku Mathematical Journal, Second Series 43(1), 3759, 1991
JSTAGE Cited by (2)

32
 Some remarks on manifolds with asymptotically nonnegative sectional curvature

YANG Y. H.
Kobe J. Math. 15, 157164, 1998
Cited by (1)