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1
V Apostolov , The
Kähler geometry of toric manifolds , (2022) arXiv:2208.12493
2
V Apostolov ,
D M J Calderbank , The CR geometry of
weighted extremal Kähler and Sasaki metrics , Math. Ann.
379 (2021) 1047 MR4238260
3
V Apostolov ,
D M J Calderbank , P Gauduchon ,
Hamiltonian
2 –forms in Kähler geometry, I :
General theory , J. Differential Geom. 73 (2006) 359
MR2228318
4
V Apostolov ,
D M J Calderbank , P Gauduchon ,
C W Tønnesen-Friedman , Hamiltonian
2 –forms in Kähler geometry, II :
Global classification , J. Differential Geom. 68 (2004)
277 MR2144249
5
V Apostolov ,
D M J Calderbank , P Gauduchon ,
C W Tønnesen-Friedman , Hamiltonian
2 –forms in Kähler geometry, IV :
Weakly Bochner-flat Kähler manifolds , Comm. Anal. Geom.
16 (2008) 91 MR2411469
6
V Apostolov ,
D M J Calderbank , P Gauduchon ,
C W Tønnesen-Friedman , Extremal Kähler
metrics on projective bundles over a curve , Adv. Math.
227 (2011) 2385 MR2807093
7
V Apostolov ,
D M J Calderbank , E Legendre ,
Weighted
K –stability of polarized varieties
and extremality of Sasaki manifolds , Adv. Math. 391
(2021) 107969 MR4300921
8
C Arezzo , F
Pacard , M Singer , Extremal metrics on
blowups , Duke Math. J. 157 (2011) 1 MR2783927
9
M F Atiyah ,
Convexity and
commuting Hamiltonians , Bull. London Math. Soc. 14
(1982) 1 MR642416
10
R J Berman ,
K –polystability of ℚ –Fano varieties admitting Kähler–Einstein
metrics , Invent. Math. 203 (2016) 973 MR3461370
11
R J Berman , B
Berndtsson , Convexity of the
K –energy on the space of Kähler
metrics and uniqueness of extremal metrics , J. Amer.
Math. Soc. 30 (2017) 1165 MR3671939
12
R J Berman , S
Boucksom , P Eyssidieux , V Guedj , A
Zeriahi , Kähler–Einstein
metrics and the Kähler–Ricci flow on log Fano
varieties , J. Reine Angew. Math. 751 (2019) 27 MR3956691
13
R J Berman , T
Darvas , C H Lu , Convexity of the
extended K –energy and the large
time behavior of the weak Calabi flow , Geom. Topol. 21
(2017) 2945 MR3687111
14
R J Berman , T
Darvas , C H Lu , Regularity of weak
minimizers of the K –energy and
applications to properness and K –stability , Ann. Sci. Éc. Norm.
Supér. 53 (2020) 267 MR4094559
15
R J Berman ,
D W Nyström , Complex optimal transport and the
pluripotential theory of Kähler–Ricci solitons , preprint
(2014) arXiv:1401.8264
16
Z Błocki , On
geodesics in the space of Kähler metrics , from: "Advances
in geometric analysis" (editors S Janeczko, J Li, D H
Phong), Adv. Lect. Math. 21, International (2012) 3 MR3077245
17
Z Błocki , S
Kołodziej , On
regularization of plurisubharmonic functions on
manifolds , Proc. Amer. Math. Soc. 135 (2007) 2089
MR2299485
18
S Boucksom , T
Hisamoto , M Jonsson , Uniform K –stability, Duistermaat–Heckman measures and
singularities of pairs , Ann. Inst. Fourier (Grenoble)
67 (2017) 743 MR3669511
19
C P Boyer , K
Galicki , S R Simanca , Canonical Sasakian
metrics , Comm. Math. Phys. 279 (2008) 705 MR2386725
20
C P Boyer ,
C W Tønnesen-Friedman , The Sasaki join,
Hamiltonian 2 –forms, and constant
scalar curvature , J. Geom. Anal. 26 (2016) 1023
MR3472828
21
E Calabi , Extremal Kähler
metrics , from: "Seminar on differential geometry"
(editor S T Yau), Ann. of Math. Stud. 102, Princeton Univ.
Press (1982) 259 MR645743
22
X Chen , The space of
Kähler metrics , J. Differential Geom. 56 (2000) 189
MR1863016
23
X Chen , J
Cheng , On the
constant scalar curvature Kähler metrics, II : Existence
results , J. Amer. Math. Soc. 34 (2021) 937 MR4301558
24
X Chen , M Paun ,
Y Zeng , On deformation of extremal metrics ,
preprint (2015) arXiv:1506.01290
25
J Chu , V
Tosatti , B Weinkove , On the C 1 , 1 regularity
of geodesics in the space of Kähler metrics , Ann. PDE 3
(2017) 15 MR3695402
26
A S Dancer ,
M Y Wang , On Ricci solitons
of cohomogeneity one , Ann. Global Anal. Geom. 39 (2011)
259 MR2769300
27
T Darvas , The Mabuchi
geometry of finite energy classes , Adv. Math. 285
(2015) 182 MR3406499
28
T Darvas , The Mabuchi completion
of the space of Kähler potentials , Amer. J. Math. 139
(2017) 1275 MR3702499
29
T Darvas , Y A
Rubinstein , Tian’s properness
conjectures and Finsler geometry of the space of Kähler
metrics , J. Amer. Math. Soc. 30 (2017) 347 MR3600039
30
V Datar , G
Székelyhidi , Kähler–Einstein
metrics along the smooth continuity method , Geom.
Funct. Anal. 26 (2016) 975 MR3558304
31
T Delcroix ,
K –stability of Fano spherical
varieties , Ann. Sci. Éc. Norm. Supér. 53 (2020) 615
MR4118525
32
F Delgove ,
Kähler–Ricci solitons on horospherical variety , preprint
(2017) arXiv:1710.05623
33
R Dervan , Relative
K –stability for Kähler
manifolds , Math. Ann. 372 (2018) 859 MR3880285
34
R Dervan , J
Ross , K –stability for Kähler manifolds ,
Math. Res. Lett. 24 (2017) 689 MR3696600
35
R Dervan , L M
Sektnan , Optimal symplectic
connections on holomorphic submersions , Comm. Pure
Appl. Math. 74 (2021) 2132 MR4303016
36
S K Donaldson ,
Lower bounds
on the Calabi functional , J. Differential Geom. 70
(2005) 453 MR2192937
37
S K Donaldson ,
Kähler geometry on toric manifolds, and some other manifolds
with large symmetry , from: "Handbook of geometric analysis"
(editors L Ji, P Li, R Schoen, L Simon), Adv. Lect. Math. 7,
International (2008) 29 MR2483362
38
A Fujiki , On automorphism groups of
compact Kähler manifolds , Invent. Math. 44 (1978) 225
MR481142
39
A Futaki , H
Ono , Conformally
Einstein–Maxwell Kähler metrics and structure of the
automorphism group , Math. Z. 292 (2019) 571 MR3968916
40
A Futaki , H
Ono , G Wang , Transverse
Kähler geometry of Sasaki manifolds and toric Sasaki–Einstein
manifolds , J. Differential Geom. 83 (2009) 585 MR2581358
41
P Gauduchon ,
Calabi’s extremal metrics : an elementary introduction ,
lecture notes, in preparation
42
J P Gauntlett ,
D Martelli , J Sparks , D Waldram ,
A new
infinite class of Sasaki–Einstein manifolds , Adv.
Theor. Math. Phys. 8 (2004) 987 MR2194373
43
V Guedj , A
Zeriahi , The weighted
Monge–Ampère energy of quasiplurisubharmonic functions ,
J. Funct. Anal. 250 (2007) 442 MR2352488
44
V Guillemin , S
Sternberg , Convexity properties of
the moment mapping , Invent. Math. 67 (1982) 491
MR664117
45
J Han , C Li ,
On the
Yau–Tian–Donaldson conjecture for generalized Kähler–Ricci
soliton equations , Comm. Pure Appl. Math. 76 (2023)
1793 MR4612573
46
Y Hashimoto ,
Existence of
twisted constant scalar curvature Kähler metrics with a large
twist , Math. Z. 292 (2019) 791 MR3980270
47
W He , On Calabi’s extremal metric
and properness , Trans. Amer. Math. Soc. 372 (2019) 5595
MR4014289
48
W He , J Li ,
Geometric
pluripotential theory on Sasaki manifolds , J. Geom.
Anal. 31 (2021) 1093 MR4215260
49
T Hisamoto ,
Stability and coercivity for toric polarizations ,
preprint (2016) arXiv:1610.07998
50
E Inoue , Constant
μ –scalar curvature Kähler
metric–formulation and foundational results , J. Geom.
Anal. 32 (2022) 145 MR4382665
51
D Jerison , J M
Lee , Extremals
for the Sobolev inequality on the Heisenberg group and the CR
Yamabe problem , J. Amer. Math. Soc. 1 (1988) 1 MR924699
52
S Jubert , A
Yau–Tian–Donaldson correspondence on a class of toric
fibrations , preprint (2021) arXiv:2108.12297
53
N Koiso , On rotationally
symmetric Hamilton’s equation for Kähler–Einstein
metrics , from: "Recent topics in differential and
analytic geometry" (editor T Ochiai), Adv. Stud. Pure Math. 18,
Academic (1990) 327 MR1145263
54
A Lahdili , Automorphisms and
deformations of conformally Kähler, Einstein–Maxwell
metrics , J. Geom. Anal. 29 (2019) 542 MR3897025
55
A Lahdili , Kähler metrics with
constant weighted scalar curvature and weighted K –stability , Proc. Lond. Math. Soc.
119 (2019) 1065 MR3964827
56
A Lahdili ,
Convexity of the weighted Mabuchi functional and the
uniqueness of weighted extremal metrics , preprint (2020)
arXiv:2007.01345
57
C Li , G –uniform stability and Kähler–Einstein
metrics on Fano varieties , Invent. Math. 227 (2022) 661
MR4372222
58
T Mabuchi , Kähler–Einstein
metrics for manifolds with nonvanishing Futaki
character , Tohoku Math. J. 53 (2001) 171 MR1829977
59
T Mabuchi , Multiplier
Hermitian structures on Kähler manifolds , Nagoya Math.
J. 170 (2003) 73 MR1994888
60
T Mabuchi , Y
Nakagawa , New examples of
Sasaki–Einstein manifolds , Tohoku Math. J. 65 (2013)
243 MR3079287
61
D Martelli , J
Sparks , S T Yau , Sasaki–Einstein
manifolds and volume minimisation , Comm. Math. Phys.
280 (2008) 611 MR2399609
62
Y Odaka , A
generalization of the Ross–Thomas slope theory , Osaka
J. Math. 50 (2013) 171 MR3080636
63
F Podestà , A
Spiro , Kähler–Ricci solitons
on homogeneous toric bundles , J. Reine Angew. Math. 642
(2010) 109 MR2658183
64
S Semmes , Complex Monge–Ampère and
symplectic manifolds , Amer. J. Math. 114 (1992) 495
MR1165352
65
Z Sjöström Dyrefelt ,
K –semistability of cscK manifolds with
transcendental cohomology class , J. Geom. Anal. 28
(2018) 2927 MR3881961
66
Z Sjöström Dyrefelt ,
On
K –polystability of cscK manifolds
with transcendental cohomology class , Int. Math. Res.
Not. 2020 (2020) 2769 MR4095424
67
J Stoppa , K –stability of constant scalar curvature
Kähler manifolds , Adv. Math. 221 (2009) 1397 MR2518643
68
J Stoppa , G
Székelyhidi , Relative K –stability of extremal metrics , J.
Eur. Math. Soc. 13 (2011) 899 MR2800479
69
A Swann , Twisting Hermitian
and hypercomplex geometries , Duke Math. J. 155 (2010)
403 MR2736170
70
G Tian , Kähler–Einstein metrics
with positive scalar curvature , Invent. Math. 130
(1997) 1 MR1471884
71
G Tian , X Zhu ,
A new
holomorphic invariant and uniqueness of Kähler–Ricci
solitons , Comment. Math. Helv. 77 (2002) 297 MR1915043
72
X Wang , Height and GIT
weight , Math. Res. Lett. 19 (2012) 909 MR3008424
73
X J Wang , X
Zhu , Kähler–Ricci
solitons on toric manifolds with positive first Chern
class , Adv. Math. 188 (2004) 87 MR2084775