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1
L Ambrosio ,
Calculus, heat flow and curvature-dimension bounds in metric
measure spaces , from: "Proceedings of the International
Congress of Mathematicians, I" (editors B Sirakov, P N de
Souza, M Viana), World Sci. (2018) 301 MR3966731
2
L Ambrosio , N
Gigli , A Mondino , T Rajala , Riemannian
Ricci curvature lower bounds in metric measure spaces with
σ –finite measure , Trans.
Amer. Math. Soc. 367 (2015) 4661 MR3335397
3
L Ambrosio , N
Gigli , G Savaré , Metric measure
spaces with Riemannian Ricci curvature bounded from
below , Duke Math. J. 163 (2014) 1405 MR3205729
4
L Ambrosio , S
Honda , J W Portegies , D Tewodrose ,
Embedding of RCD ∗ ( K,N ) spaces in L 2 via
eigenfunctions , preprint (2018) arXiv:1812.03712
5
L Ambrosio , A
Mondino , G Savaré , Nonlinear diffusion
equations and curvature conditions in metric measure
spaces , 1270, Amer. Math. Soc. (2019) MR4044464
6
G Antonelli , E
Brué , D Semola , Volume bounds for the
quantitative singular strata of non collapsed RCD metric
measure spaces , Anal. Geom. Metr. Spaces 7 (2019) 158
MR4015195
7
K Bacher , K T
Sturm , Localization and
tensorization properties of the curvature-dimension condition
for metric measure spaces , J. Funct. Anal. 259 (2010)
28 MR2610378
8
D Barilari , L
Rizzi , Sharp measure
contraction property for generalized H –type Carnot groups , Commun. Contemp.
Math. 20 (2018) MR3848070
9
J Bertrand ,
Pincement spectral
en courbure de Ricci positive , Comment. Math. Helv. 82
(2007) 323 MR2319931
10
S Bianchini , F
Cavalletti , The Monge problem
for distance cost in geodesic spaces , Comm. Math. Phys.
318 (2013) 615 MR3027581
11
E Brué , D
Semola , Constancy of the dimension
for RCD ( K,N ) spaces via regularity of Lagrangian
flows , Comm. Pure Appl. Math. 73 (2020) 1141
12
F Cavalletti ,
Monge
problem in metric measure spaces with Riemannian
curvature-dimension condition , Nonlinear Anal. 99
(2014) 136 MR3160530
13
F Cavalletti , E
Milman , The globalization theorem for the curvature
dimension condition , preprint (2016) arXiv:1612.07623
14
F Cavalletti , A
Mondino , Measure rigidity of
Ricci curvature lower bounds , Adv. Math. 286 (2016) 430
MR3415690
15
F Cavalletti , A
Mondino , Optimal maps in
essentially non-branching spaces , Commun. Contemp.
Math. 19 (2017) MR3691502
16
F Cavalletti , A
Mondino , New formulas for
the Laplacian of distance functions and applications ,
Anal. PDE 13 (2020) 2091 MR4175820
17
J Cheeger , T H
Colding , On the structure of
spaces with Ricci curvature bounded below, I , J.
Differential Geom. 46 (1997) 406 MR1484888
18
J Cheeger , T H
Colding , On the structure of
spaces with Ricci curvature bounded below, II , J.
Differential Geom. 54 (2000) 13 MR1815410
19
J Cheeger , T H
Colding , On the structure of
spaces with Ricci curvature bounded below, III , J.
Differential Geom. 54 (2000) 37 MR1815411
20
J Cheeger , W
Jiang , A Naber , Rectifiability of singular sets
in noncollapsed spaces with Ricci curvature bounded below ,
preprint (2018) arXiv:1805.07988
21
J Cheeger , A
Naber , Lower bounds on
Ricci curvature and quantitative behavior of singular
sets , Invent. Math. 191 (2013) 321 MR3010378
22
J Cheeger , A
Naber , Regularity of
Einstein manifolds and the codimension 4 conjecture , Ann. of Math. 182 (2015)
1093 MR3418535
23
T H Colding ,
Large
manifolds with positive Ricci curvature , Invent. Math.
124 (1996) 193 MR1369415
24
T H Colding ,
Shape of
manifolds with positive Ricci curvature , Invent. Math.
124 (1996) 175 MR1369414
25
T H Colding ,
Ricci curvature
and volume convergence , Ann. of Math. 145 (1997) 477
MR1454700
26
G De Philippis , N
Gigli , Non-collapsed spaces with
Ricci curvature bounded from below , J. Éc. Polytech.
Math. 5 (2018) 613 MR3852263
27
G De Philippis , A
Marchese , F Rindler , On a conjecture of
Cheeger , from: "Measure theory in non-smooth spaces"
(editor N Gigli), de Gruyter (2017) 145 MR3701738
28
S Donaldson , S
Sun , Gromov–Hausdorff
limits of Kähler manifolds and algebraic geometry, II ,
J. Differential Geom. 107 (2017) 327 MR3707646
29
M Erbar , K
Kuwada , K T Sturm , On the equivalence
of the entropic curvature-dimension condition and Bochner’s
inequality on metric measure spaces , Invent. Math. 201
(2015) 993 MR3385639
30
M Erbar , K T
Sturm , Rigidity of cones with
bounded Ricci curvature , J. Eur. Math. Soc. 23 (2021)
219 MR4186467
31
F Galaz-García , M
Kell , A Mondino , G Sosa , On quotients of
spaces with Ricci curvature bounded below , J. Funct.
Anal. 275 (2018) 1368 MR3820328
32
N Gigli , An overview of the
proof of the splitting theorem in spaces with non-negative
Ricci curvature , Anal. Geom. Metr. Spaces 2 (2014) 169
MR3210895
33
N Gigli , On the differential
structure of metric measure spaces and applications ,
1113, Amer. Math. Soc. (2015) MR3381131
34
N Gigli , A
Mondino , G Savaré , Convergence of pointed
non-compact metric measure spaces and stability of Ricci
curvature bounds and heat flows , Proc. Lond. Math. Soc.
111 (2015) 1071 MR3477230
35
N Gigli , E
Pasqualetto , Behaviour of the reference measure on RCD
spaces under charts , preprint (2016) arXiv:1607.05188
36
B X Han ,
Measure
rigidity of synthetic lower Ricci curvature bound on Riemannian
manifolds , Adv. Math. 373 (2020) MR4129481
37
S Honda , New differential
operator and noncollapsed RCD spaces , Geom. Topol. 24
(2020) 2127 MRMR4173928
38
S Honda , I
Mondello , Sphere theorems for RCD and stratified
spaces , preprint (2019) arXiv:1907.03482
39
N Juillet , Geometric inequalities
and generalized Ricci bounds in the Heisenberg group ,
Int. Math. Res. Not. 2009 (2009) 2347 MR2520783
40
V Kapovitch ,
Perelman’s
stability theorem , from: "Surveys in differential
geometry, XI" (editors J Cheeger, K Grove), International
(2007) 103 MR2408265
41
V Kapovitch , C
Ketterer , CD meets
CAT , J. Reine Angew. Math. 766 (2020) 1 MR4145200
42
V Kapovitch , A
Lytchak , A Petrunin , Metric-measure boundary and
geodesic flow on Alexandrov spaces , J. Eur. Math. Soc.
23 (2021) 29 MR4186463
43
M Kell , A
Mondino , On the volume
measure of non-smooth spaces with Ricci curvature bounded
below , Ann. Sc. Norm. Super. Pisa Cl. Sci. 18 (2018)
593 MR3801291
44
C Ketterer ,
Cones
over metric measure spaces and the maximal diameter
theorem , J. Math. Pures Appl. 103 (2015) 1228 MR3333056
45
C Ketterer ,
Obata’s
rigidity theorem for metric measure spaces , Anal. Geom.
Metr. Spaces 3 (2015) 278 MR3403434
46
R C Kirby ,
L C Siebenmann , Foundational essays
on topological manifolds, smoothings, and
triangulations , 88, Princeton Univ. Press (1977)
MR0645390
47
Y Kitabeppu ,
A Bishop-type
inequality on metric measure spaces with Ricci curvature
bounded below , Proc. Amer. Math. Soc. 145 (2017) 3137
MR3637960
48
Y Kitabeppu ,
A
sufficient condition to a regular set being of positive measure
on RCD spaces , Potential Anal. 51 (2019) 179 MR3983504
49
Y Kitabeppu , S
Lakzian , Characterization of
low dimensional RCD ∗ ( K,N ) spaces , Anal. Geom. Metr. Spaces 4
(2016) 187 MR3550295
50
J Lott , C
Villani , Ricci curvature
for metric-measure spaces via optimal transport , Ann.
of Math. 169 (2009) 903 MR2480619
51
A Lytchak , S
Stadler , Ricci curvature in dimension 2 , preprint (2018) arXiv:1812.08225
52
A Mondino , A
Naber , Structure theory of metric
measure spaces with lower Ricci curvature bounds , J.
Eur. Math. Soc. 21 (2019) 1809 MR3945743
53
S i Ohta ,
On the measure
contraction property of metric measure spaces , Comment.
Math. Helv. 82 (2007) 805 MR2341840
54
S i Ohta ,
Finsler
interpolation inequalities , Calc. Var. Partial
Differential Equations 36 (2009) 211 MR2546027
55
G Perelman ,
Alexandrov’s spaces
with curvatures bounded from below, II , preprint
(1991)
56
P Petersen ,
On
eigenvalue pinching in positive Ricci curvature ,
Invent. Math. 138 (1999) 1 MR1714334
57
A Petrunin ,
Parallel
transportation for Alexandrov space with curvature bounded
below , Geom. Funct. Anal. 8 (1998) 123 MR1601854
58
A Petrunin ,
Alexandrov meets Lott–Villani–Sturm , Münster J. Math. 4
(2011) 53 MR2869253
59
F Quinn , Ends of maps, III :
Dimensions 4 and 5 , J. Differential Geom. 17 (1982) 503
MR679069
60
T Rajala , K T
Sturm , Non-branching
geodesics and optimal maps in strong CD ( K, ∞ ) –spaces , Calc. Var. Partial
Differential Equations 50 (2014) 831 MR3216835
61
L Rifford , Ricci curvatures in
Carnot groups , Math. Control Relat. Fields 3 (2013) 467
MR3110060
62
L Rizzi , Measure contraction
properties of Carnot groups , Calc. Var. Partial
Differential Equations 55 (2016) MR3502622
63
L C Siebenmann ,
Deformation of
homeomorphisms on stratified sets , Comment. Math. Helv.
47 (1972) 123 MR319207
64
M Simon , Ricci flow of
non-collapsed three manifolds whose Ricci curvature is bounded
from below , J. Reine Angew. Math. 662 (2012) 59
MR2876261
65
M Simon , P M
Topping , Local mollification of Riemannian metrics using
Ricci flow, and Ricci limit spaces , preprint (2017)
arXiv:1706.09490
66
K T Sturm ,
On the
geometry of metric measure spaces, I , Acta Math. 196
(2006) 65 MR2237206
67
K T Sturm ,
On the
geometry of metric measure spaces, II , Acta Math. 196
(2006) 133 MR2237207
68
C Villani , Optimal transport:
old and new , 338, Springer (2009) MR2459454
69
C Villani , Inégalités isopérimétriques dans
les espaces métriques mesurés (d’après F Cavalletti & A
Mondino) , from: "Séminaire Bourbaki, 2016/2017",
Astérisque 407, Soc. Math. France (2019) 213 MR3939278
70
J Wong , An extension
procedure for manifolds with boundary , Pacific J. Math.
235 (2008) 173 MR2379775