Volume 18, issue 2 (2014)

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

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

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
Editorial Board
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
A weakly second-order differential structure on rectifiable metric measure spaces

Shouhei Honda

Geometry & Topology 18 (2014) 633–668
Bibliography
1 L Ambrosio, B Kirchheim, Currents in metric spaces, Acta Math. 185 (2000) 1 MR1794185
2 Y Burago, M Gromov, G Perelman, A D Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk 47 (1992) 3 MR1185284
3 J Cheeger, Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal. 9 (1999) 428 MR1708448
4 J Cheeger, Degeneration of Riemannian metrics under Ricci curvature bounds, Lezioni Fermiane, Scuola Normale Superiore (2001) MR2006642
5 J Cheeger, T H Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. 144 (1996) 189 MR1405949
6 J Cheeger, T H Colding, On the structure of spaces with Ricci curvature bounded below, I, J. Differential Geom. 46 (1997) 406 MR1484888
7 J Cheeger, T H Colding, On the structure of spaces with Ricci curvature bounded below, II, J. Differential Geom. 54 (2000) 13 MR1815410
8 J Cheeger, T H Colding, On the structure of spaces with Ricci curvature bounded below, III, J. Differential Geom. 54 (2000) 37 MR1815411
9 S Y Cheng, S T Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975) 333 MR0385749
10 T H Colding, A Naber, Lower Ricci curvature, branching and bi-Lipschitz structure of uniform Reifenberg spaces arXiv:1111.2184
11 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
12 Y Ding, Heat kernels and Green's functions on limit spaces, Comm. Anal. Geom. 10 (2002) 475 MR1912256
13 K Fukaya, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent. Math. 87 (1987) 517 MR874035
14 M Gromov, Metric structures for Riemannian and non-Riemannian spaces, Birkhäuser (2007) MR2307192
15 S Honda, Ricci curvature and $L^p$–convergence, to appear in J. Reine Angew. Math. arXiv:1212.2052
16 S Honda, Bishop–Gromov type inequality on Ricci limit spaces, J. Math. Soc. Japan 63 (2011) 419 MR2793106
17 S Honda, Ricci curvature and convergence of Lipschitz functions, Comm. Anal. Geom. 19 (2011) 79 MR2818407
18 A Kasue, Convergence of Riemannian manifolds and Laplace operators, I, Ann. Inst. Fourier (Grenoble) 52 (2002) 1219 MR1927079
19 A Kasue, Convergence of Riemannian manifolds and Laplace operators, II, Potential Anal. 24 (2006) 137 MR2217418
20 A Kasue, H Kumura, Spectral convergence of Riemannian manifolds, Tohoku Math. J. 46 (1994) 147 MR1272877
21 A Kasue, H Kumura, Spectral convergence of Riemannian manifolds, II, Tohoku Math. J. 48 (1996) 71 MR1373175
22 S Keith, A differentiable structure for metric measure spaces, Adv. Math. 183 (2004) 271 MR2041901
23 K Kuwae, T Shioya, Convergence of spectral structures: A functional analytic theory and its applications to spectral geometry, Comm. Anal. Geom. 11 (2003) 599 MR2015170
24 T J Laakso, Ahlfors $Q$–regular spaces with arbitrary $Q\gt 1$ admitting weak Poincaré inequality, Geom. Funct. Anal. 10 (2000) 111 MR1748917
25 J Lott, C Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. 169 (2009) 903 MR2480619
26 S i Ohta, On the measure contraction property of metric measure spaces, Comment. Math. Helv. 82 (2007) 805 MR2341840
27 Y Otsu, Almost everywhere existence of second differentiable structure of Alexandrov spaces, preprint
28 Y Otsu, T Shioya, The Riemannian structure of Alexandrov spaces, J. Differential Geom. 39 (1994) 629 MR1274133
29 P Pansu, Métriques de Carnot–Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. 129 (1989) 1 MR979599
30 G Perelman, A D Alexandrov spaces with curvature bounded from below, II, preprint
31 G Perelman, DC–structure on Alexandrov space
32 H Rademacher, Über partielle und totale differenzierbarkeit von Funktionen mehrerer Variabeln und über die Transformation der Doppelintegrale, Math. Ann. 79 (1919) 340 MR1511935
33 L Simon, Lectures on geometric measure theory, Proc. Cent. Math. Anal. Austr. Nat. Uni. 3, Australian National University Centre for Mathematical Analysis (1983) MR756417
34 K T Sturm, On the geometry of metric measure spaces, I, Acta Math. 196 (2006) 65 MR2237206
35 K T Sturm, On the geometry of metric measure spaces, II, Acta Math. 196 (2006) 133 MR2237207
36 C Villani, Optimal transport: Old and new, Grundl. Math. Wissen. 338, Springer (2009) MR2459454