Volume 23, issue 6 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 27
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Inradius collapsed manifolds

Takao Yamaguchi and Zhilang Zhang

Geometry & Topology 23 (2019) 2793–2860
Bibliography
1 S B Alexander, R L Bishop, Thin Riemannian manifolds with boundary, Math. Ann. 311 (1998) 55 MR1624263
2 M Anderson, A Katsuda, Y Kurylev, M Lassas, M Taylor, Boundary regularity for the Ricci equation, geometric convergence, and Gel’fand’s inverse boundary problem, Invent. Math. 158 (2004) 261 MR2096795
3 D Burago, Y Burago, S Ivanov, A course in metric geometry, 33, Amer. Math. Soc. (2001) MR1835418
4 Y Burago, M Gromov, G Perelman, A D Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk 47 (1992) 3, 222 MR1185284
5 J Cheeger, T H Colding, On the structure of spaces with Ricci curvature bounded below, I, J. Differential Geom. 46 (1997) 406 MR1484888
6 J Cheeger, T H Colding, On the structure of spaces with Ricci curvature bounded below, II, J. Differential Geom. 54 (2000) 13 MR1815410
7 J Cheeger, K Fukaya, M Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992) 327 MR1126118
8 T H Colding, A Naber, Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications, Ann. of Math. 176 (2012) 1173 MR2950772
9 K Fukaya, T Yamaguchi, The fundamental groups of almost non-negatively curved manifolds, Ann. of Math. 136 (1992) 253 MR1185120
10 M Gromov, Synthetic geometry in Riemannian manifolds, from: "Proceedings of the International Congress of Mathematicians" (editor O Lehto), Acad. Sci. Fennica (1980) 415 MR562635
11 J Harvey, C Searle, Orientation and symmetries of Alexandrov spaces with applications in positive curvature, J. Geom. Anal. 27 (2017) 1636 MR3625167
12 V Kapovitch, Regularity of limits of noncollapsing sequences of manifolds, Geom. Funct. Anal. 12 (2002) 121 MR1904560
13 V Kapovitch, Perelman’s stability theorem, from: "Metric and comparison geometry" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, International (2007) 103 MR2408265
14 V Kapovitch, A Petrunin, W Tuschmann, Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces, Ann. of Math. 171 (2010) 343 MR2630041
15 V Kapovitch, B Wilking, Structure of fundamental groups of manifolds with Ricci curvature bounded below, preprint (2011) arXiv:1105.5955
16 S Kodani, Convergence theorem for Riemannian manifolds with boundary, Compositio Math. 75 (1990) 171 MR1065204
17 N N Kosovskiĭ, Gluing of Riemannian manifolds of curvature κ, Algebra i Analiz 14 (2002) 140 MR1921991
18 A Mitsuishi, T Yamaguchi, Collapsing three-dimensional Alexandrov spaces with boundary, in preparation
19 A Mitsuishi, T Yamaguchi, Collapsing three-dimensional closed Alexandrov spaces with a lower curvature bound, Trans. Amer. Math. Soc. 367 (2015) 2339 MR3301867
20 Y Otsu, T Shioya, The Riemannian structure of Alexandrov spaces, J. Differential Geom. 39 (1994) 629 MR1274133
21 G Perelman, Alexandrov spaces with curvature bounded below, II, preprint (1991)
22 G Y Perelman, Elements of Morse theory on Aleksandrov spaces, Algebra i Analiz 5 (1993) 232 MR1220498
23 G Y Perelman, A M Petrunin, Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem, Algebra i Analiz 5 (1993) 242 MR1220499
24 G Perelman, A Petrunin, Quasigeodesics and gradient curves in Alexandrov spaces, preprint (1995)
25 A Petrunin, Parallel transportation for Alexandrov space with curvature bounded below, Geom. Funct. Anal. 8 (1998) 123 MR1601854
26 A Petrunin, Semiconcave functions in Alexandrov’s geometry, from: "Metric and comparison geometry" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, International (2007) 137 MR2408266
27 T Shioya, T Yamaguchi, Collapsing three-manifolds under a lower curvature bound, J. Differential Geom. 56 (2000) 1 MR1863020
28 T Shioya, T Yamaguchi, Volume collapsed three-manifolds with a lower curvature bound, Math. Ann. 333 (2005) 131 MR2169831
29 J A Wong, Collapsing manifolds with boundary, PhD thesis, University of Illinois at Urbana-Champaign (2006) MR2709656
30 J Wong, An extension procedure for manifolds with boundary, Pacific J. Math. 235 (2008) 173 MR2379775
31 J Wong, Collapsing manifolds with boundary, Geom. Dedicata 149 (2010) 291 MR2737694
32 T Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. 133 (1991) 317 MR1097241
33 T Yamaguchi, A convergence theorem in the geometry of Alexandrov spaces, from: "Actes de la table ronde de géométrie différentielle" (editor A L Besse), Sémin. Congr. 1, Soc. Mat. de France (1996) 601 MR1427772
34 T Yamaguchi, Collapsing 4–manifolds under a lower curvature bound, preprint (2012) arXiv:1205.0323
35 T Yamaguchi, Z Zhang, Convergence of manifolds with boundary, in preparation