Geometry & Topology Volume 23, issue 6 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Metric-minimizing surfaces revisited

Anton Petrunin and Stephan Stadler

Geometry & Topology 23 (2019) 3111–3139

DOI: 10.2140/gt.2019.23.3111

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