Volume 23, issue 6 (2019)

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

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

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
Metric-minimizing surfaces revisited

Anton Petrunin and Stephan Stadler

Geometry & Topology 23 (2019) 3111–3139
Bibliography
1 A D Aleksandrov, Ruled surfaces in metric spaces, Vestnik Leningrad. Univ. 12 (1957) 5 MR0085564
2 S B Alexander, R L Bishop, Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above, Geom. Dedicata 117 (2006) 65 MR2231159
3 S Alexander, V Kapovitch, A Petrunin, An invitation to Alexandrov geometry : CAT(0) spaces, Springer (2019) MR3930625
4 T Banakh, Running most of the time in a connected set, MathOverflow post (2018)
5 A Bressan, Hyperbolic systems of conservation laws: the one-dimensional Cauchy problem, 20, Oxford Univ. Press (2000) MR1816648
6 D Burago, Y Burago, S Ivanov, A course in metric geometry, 33, Amer. Math. Soc. (2001) MR1835418
7 R J Daverman, Decompositions of manifolds, 124, Academic (1986) MR872468
8 M Gromov, Singularities, expanders and topology of maps, I : Homology versus volume in the spaces of cycles, Geom. Funct. Anal. 19 (2009) 743 MR2563769
9 A N Kolmogorov, S V Fomin, Элементю теории функщии и функщионального анализа, Izdat. “Nauka” (1976) 543 MR0435771
10 N J Korevaar, R M Schoen, Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom. 1 (1993) 561 MR1266480
11 U Lang, V Schroeder, Kirszbraun’s theorem and metric spaces of bounded curvature, Geom. Funct. Anal. 7 (1997) 535 MR1466337
12 E Le Donne, Lipschitz and path isometric embeddings of metric spaces, Geom. Dedicata 166 (2013) 47 MR3101160
13 A Lytchak, On the geometry of subsets of positive reach, Manuscripta Math. 115 (2004) 199 MR2098470
14 A Lytchak, S Stadler, Conformal deformations of CAT(0) spaces, Math. Ann. 373 (2019) 155 MR3968869
15 A Lytchak, S Wenger, Area minimizing discs in metric spaces, Arch. Ration. Mech. Anal. 223 (2017) 1123 MR3594354
16 A Lytchak, S Wenger, Intrinsic structure of minimal discs in metric spaces, Geom. Topol. 22 (2018) 591 MR3720351
17 A Lytchak, S Wenger, Isoperimetric characterization of upper curvature bounds, Acta Math. 221 (2018) 159 MR3877021
18 C Mese, The curvature of minimal surfaces in singular spaces, Comm. Anal. Geom. 9 (2001) 3 MR1807950
19 R L Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925) 416 MR1501320
20 A Petrunin, Metric minimizing surfaces, Electron. Res. Announc. Amer. Math. Soc. 5 (1999) 47 MR1679453
21 A Petrunin, Intrinsic isometries in Euclidean space, Algebra i Analiz 22 (2010) 140 MR2828830
22 A Petrunin, Correction to : Metric minimizing surfaces, Electron. Res. Announc. Math. Sci. 25 (2018) 96 MR3915541
23 A Petrunin, S Stadler, Monotonicity of saddle maps, Geom. Dedicata 198 (2019) 181 MR3933457
24 S Z Shefel, On the intrinsic geometry of saddle surfaces, Sibirsk. Mat. Ž. 5 (1964) 1382 MR0175046
25 S Z Shefel, On saddle surfaces bounded by a rectifiable curve, Dokl. Akad. Nauk SSSR 162 (1965) 294 MR0179700
26 S Stadler, The structure of minimal surfaces in CAT(0) spaces, preprint (2018) arXiv:1808.06410