Geometry & Topology Volume 27, issue 9 (2023)

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

The Gromov–Hausdorff distance between spheres

Sunhyuk Lim, Facundo Mémoli and Zane Smith

Geometry & Topology 27 (2023) 3733–3800

DOI: 10.2140/gt.2023.27.3733

Bibliography

1	H Adams, S Chowdhury, A Q Jaffe, B Sibanda, Vietoris–Rips complexes of regular polygons, preprint (2018) arXiv:1807.10971
2	I Bogdanov, Gromov–Hausdorff distance between a disk and a circle, MathOverflow answer (2018)
3	A M Bronstein, M M Bronstein, R Kimmel, Numerical geometry of non-rigid shapes, Springer (2008) MR2493634
4	D Burago, Y Burago, S Ivanov, A course in metric geometry, 33, Amer. Math. Soc. (2001) MR1835418
5	G Carlsson, Topology and data, Bull. Amer. Math. Soc. 46 (2009) 255 MR2476414
6	G Carlsson, Topological pattern recognition for point cloud data, Acta Numer. 23 (2014) 289 MR3202240
7	G Carlsson, F Mémoli, Characterization, stability and convergence of hierarchical clustering methods, J. Mach. Learn. Res. 11 (2010) 1425 MR2645457
8	M Cho, On the optimal covering of equal metric balls in a sphere, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 4 (1997) 137 MR1603755
9	S Chowdhury, F Mémoli, Explicit geodesics in Gromov–Hausdorff space, Electron. Res. Announc. Math. Sci. 25 (2018) 48 MR3824738
10	T H Colding, Large manifolds with positive Ricci curvature, Invent. Math. 124 (1996) 193 MR1369415
11	L E Dubins, G Schwarz, Equidiscontinuity of Borsuk–Ulam functions, Pacific J. Math. 95 (1981) 51 MR631658
12	D A Edwards, The structure of superspace, from: "Studies in topology" (editors N M Stavrakas, K R Allen), Academic (1975) 121 MR401069
13	G B Folland, Real analysis: modern techniques and their applications, John Wiley and Sons (1999) MR1681462
14	K Funano, Estimates of Gromov’s box distance, Proc. Amer. Math. Soc. 136 (2008) 2911 MR2399058
15	A Gray, Tubes, 221, Birkhäuser (2004) MR2024928
16	M Gromov, Metric structures for Riemannian and non-Riemannian spaces, 152, Birkhäuser (1999) MR1699320
17	Y Ji, A A Tuzhilin, Gromov–Hausdorff distance between interval and circle, Topology Appl. 307 (2022) 107938 MR4356690
18	N J Kalton, M I Ostrovskii, Distances between Banach spaces, Forum Math. 11 (1999) 17 MR1673915
19	M Katz, The filling radius of two-point homogeneous spaces, J. Differential Geom. 18 (1983) 505 MR723814
20	M G Katz, Torus cannot collapse to a segment, J. Geom. 111 (2020) 13 MR4069827
21	S Lim, F Mémoli, O B Okutan, Vietoris–Rips persistent homology, injective metric spaces, and the filling radius, preprint (2020) arXiv:2001.07588
22	S Lim, F Mémoli, Z Smith, GitHub repository
23	S Lim, F Mémoli, Z Smith, The Gromov–Hausdorff distance between spheres, preprint (2021) arXiv:2105.00611
24	J Matoušek, Using the Borsuk–Ulam theorem : lectures on topological methods in combinatorics and geometry, Springer (2003) MR1988723
25	F Mémoli, Gromov–Wasserstein distances and the metric approach to object matching, Found. Comput. Math. 11 (2011) 417 MR2811584
26	F Mémoli, Some properties of Gromov–Hausdorff distances, Discrete Comput. Geom. 48 (2012) 416 MR2946454
27	F Mémoli, G Sapiro, A theoretical and computational framework for isometry invariant recognition of point cloud data, Found. Comput. Math. 5 (2005) 313 MR2168679
28	H J Munkholm, A Borsuk–Ulam theorem for maps from a sphere to a compact topological manifold, Illinois J. Math. 13 (1969) 116 MR238324
29	G Peano, Sur une courbe, qui remplit toute une aire plane, Math. Ann. 36 (1890) 157 MR1510617
30	P Petersen, Riemannian geometry, 171, Springer (1998) MR1480173
31	L A Santaló, Convex regions on the n–dimensional spherical surface, Ann. of Math. 47 (1946) 448 MR17562