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

Volume 30
Issue 7, 2431–2778
Issue 6, 2043–2429
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Two-dimensional metric spaces with curvature bounded above, I

Koichi Nagano, Takashi Shioya and Takao Yamaguchi

Geometry & Topology 28 (2024) 3023–3093
Bibliography
1 A D Aleksandrov, Ruled surfaces in metric spaces, Vestnik Leningrad. Univ. 12 (1957) 5 MR0085564
2 A D Aleksandrov, Über eine Verallgemeinerung der Riemannschen Geometrie, Schr. Forschungsinst. Math. 1 (1957) 33 MR0087119
3 A D Aleksandrov, V A Zalgaller, Intrinsic geometry of surfaces, 15, Amer. Math. Soc. (1967) MR0216434
4 S Alexander, R Bishop, R Ghrist, Total curvature and simple pursuit on domains of curvature bounded above, Geom. Dedicata 149 (2010) 275 MR2737693
5 S Alexander, V Kapovitch, A Petrunin, Alexandrov geometry: foundations, 236, Amer. Math. Soc. (2024) MR4734965
6 C D Aliprantis, O Burkinshaw, Principles of real analysis, North-Holland (1981) MR607327
7 I A Arshinova, S V Buyalo, Metrics with upper-bounded curvature on 2–polyhedra, Algebra i Analiz 8 (1996) 163 MR1428989
8 W Ballmann, Lectures on spaces of nonpositive curvature, 25, Birkhäuser (1995) MR1377265
9 W Ballmann, S Buyalo, Nonpositively curved metrics on 2–polyhedra, Math. Z. 222 (1996) 97 MR1388005
10 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
11 D Burago, Y Burago, S Ivanov, A course in metric geometry, 33, Amer. Math. Soc. (2001) MR1835418
12 Y D Burago, S V Buyalo, Metrics with upper-bounded curvature on 2–polyhedra, II, Algebra i Analiz 10 (1998) 62 MR1654071
13 Y Burago, M Gromov, G Perelman, A D Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk 47 (1992) 3 MR1185284
14 K Grove, P Petersen V, J Y Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990) 205 MR1029396
15 B Kleiner, The local structure of length spaces with curvature bounded above, Math. Z. 231 (1999) 409 MR1704987
16 L Kramer, On the local structure and the homology of CAT(κ) spaces and Euclidean buildings, Adv. Geom. 11 (2011) 347 MR2795430
17 A Lytchak, K Nagano, Geodesically complete spaces with an upper curvature bound, Geom. Funct. Anal. 29 (2019) 295 MR3925112
18 A Lytchak, V Schroeder, Affine functions on CAT(κ)–spaces, Math. Z. 255 (2007) 231 MR2262730
19 A Lytchak, S Stadler, Improvements of upper curvature bounds, Trans. Amer. Math. Soc. 373 (2020) 7153 MR4155203
20 A Lytchak, S Stadler, Curvature bounds of subsets in dimension two, J. Differential Geom. 127 (2024) 1245
21 K Nagano, Asymptotic rigidity of Hadamard 2–spaces, J. Math. Soc. Japan 52 (2000) 699 MR1774626
22 K Nagano, A sphere theorem for 2–dimensional CAT(1)–spaces, Pacific J. Math. 206 (2002) 401 MR1926784
23 K Nagano, A volume convergence theorem for Alexandrov spaces with curvature bounded above, Math. Z. 241 (2002) 127 MR1930988
24 K Nagano, T Shioya, T Yamaguchi, Two-dimensional metric spaces with curvature bounded above, II, preprint (2023) arXiv:2308.16398
25 Y Otsu, H Tanoue, The Riemannian structure of Alexandrov spaces with curvature bounded above, preprint (1999)
26 A Petrunin, S Stadler, Metric-minimizing surfaces revisited, Geom. Topol. 23 (2019) 3111 MR4039186
27 Y G Reshetnyak, On the theory of spaces with curvature no greater than K, Mat. Sb. 52(94) (1960) 789 MR0121762
28 Y G Reshetnyak, Two-dimensional manifolds of bounded curvature, from: "Geometry, IV", Encycl. Math. Sci. 70, Springer (1993) 3 MR1263964
29 S Stadler, The structure of minimal surfaces in CAT(0) spaces, J. Eur. Math. Soc. 23 (2021) 3521 MR4310811
30 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. Math. France (1996) 601 MR1427772
31 T Yamaguchi, Upper curvature bounds and singularities, from: "Noncommutativity and singularities" (editors J P Bourguignon, M Kotani, Y Maeda, N Tose), Adv. Stud. Pure Math. 55, Math. Soc. Japan (2009) 161 MR2463496
32 T Yamaguchi, Z Zhang, Limits of manifolds with boundary, preprint (2024) arXiv:2406.00970