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

Volume 28
Issue 7, 3001–3510
Issue 6, 2483–2999
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 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Classification results for expanding and shrinking gradient Kähler–Ricci solitons

Ronan J Conlon, Alix Deruelle and Song Sun

Geometry & Topology 28 (2024) 267–351
Bibliography
1 D M Austin, P J Braam, Morse–Bott theory and equivariant cohomology, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 123 MR1362827
2 W Ballmann, Lectures on Kähler manifolds, Eur. Math. Soc. (2006) MR2243012
3 W Barth, R Narasimhan, editors, Several complex variables, VI : Complex manifolds, 69, Springer (1990) MR1095088
4 F A Belgun, On the metric structure of non-Kähler complex surfaces, Math. Ann. 317 (2000) 1 MR1760667
5 N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, 298, Springer (2004) MR2273508
6 R J Berman, D W Nystrom, Complex optimal transport and the pluripotential theory of Kähler–Ricci solitons, preprint (2014) arXiv:1401.8264
7 C Birkar, P Cascini, C D Hacon, J McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010) 405 MR2601039
8 C P Boyer, K Galicki, Sasakian geometry, Oxford Univ. Press (2008) MR2382957
9 E Brieskorn, Rationale Singularitäten komplexer Flächen, Invent. Math. 4 (1967/68) 336 MR0222084
10 R L Bryant, Gradient Kähler Ricci solitons, from: "Géométrie différentielle, physique mathématique, mathématiques et société, I" (editor O Hijazi), Astérisque 321, Soc. Math. France (2008) 51 MR2521644
11 H D Cao, D Zhou, On complete gradient shrinking Ricci solitons, J. Differential Geom. 85 (2010) 175 MR2732975
12 C W Chen, A Deruelle, Structure at infinity of expanding gradient Ricci soliton, Asian J. Math. 19 (2015) 933 MR3431684
13 X Chen, S Sun, G Tian, A note on Kähler–Ricci soliton, Int. Math. Res. Not. 2009 (2009) 3328 MR2535001
14 B Chow, D Knopf, The Ricci flow : an introduction, 110, Amer. Math. Soc. (2004) MR2061425
15 B Chow, P Lu, Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay, C. R. Math. Acad. Sci. Paris 353 (2015) 1007 MR3419851
16 B Chow, P Lu, B Yang, Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons, C. R. Math. Acad. Sci. Paris 349 (2011) 1265 MR2861997
17 C van Coevering, Examples of asymptotically conical Ricci-flat Kähler manifolds, Math. Z. 267 (2011) 465 MR2772262
18 T C Collins, G Székelyhidi, K–semistability for irregular Sasakian manifolds, J. Differential Geom. 109 (2018) 81 MR3798716
19 R J Conlon, A Deruelle, Expanding Kähler–Ricci solitons coming out of Kähler cones, J. Differential Geom. 115 (2020) 303 MR4100705
20 R J Conlon, H J Hein, Asymptotically conical Calabi–Yau manifolds, I, Duke Math. J. 162 (2013) 2855 MR3161306
21 R J Conlon, H J Hein, Asymptotically conical Calabi–Yau metrics on quasi-projective varieties, Geom. Funct. Anal. 25 (2015) 517 MR3334234
22 X Dai, G Wei, Comparison geometry for Ricci curvature, online book (2008)
23 A S Dancer, M Y Wang, On Ricci solitons of cohomogeneity one, Ann. Global Anal. Geom. 39 (2011) 259 MR2769300
24 J P Demailly, Complex analytic and differential geometry, online book (2012)
25 J P Demailly, M Paun, Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. 159 (2004) 1247 MR2113021
26 A Deruelle, Smoothing out positively curved metric cones by Ricci expanders, Geom. Funct. Anal. 26 (2016) 188 MR3494489
27 A Deruelle, Asymptotic estimates and compactness of expanding gradient Ricci solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci. 17 (2017) 485 MR3700376
28 J J Duistermaat, G J Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982) 259 MR0674406
29 F Fang, X D Li, Z Zhang, Two generalizations of Cheeger–Gromoll splitting theorem via Bakry–Emery Ricci curvature, Ann. Inst. Fourier (Grenoble) 59 (2009) 563 MR2521428
30 M Feldman, T Ilmanen, D Knopf, Rotationally symmetric shrinking and expanding gradient Kähler–Ricci solitons, J. Differential Geom. 65 (2003) 169 MR2058261
31 T Frankel, Fixed points and torsion on Kähler manifolds, Ann. of Math. 70 (1959) 1 MR0131883
32 A Futaki, Kähler–Einstein metrics and integral invariants, 1314, Springer (1988) MR0947341
33 A Futaki, The weighted Laplacians on real and complex metric measure spaces, from: "Geometry and analysis on manifolds" (editors T Ochiai, T Mabuchi, Y Maeda, J Noguchi, A Weinstein), Progr. Math. 308, Springer (2015) 343 MR3331404
34 A Futaki, M T Wang, Constructing Kähler–Ricci solitons from Sasaki–Einstein manifolds, Asian J. Math. 15 (2011) 33 MR2786464
35 A M Gleason, R S Palais, On a class of transformation groups, Amer. J. Math. 79 (1957) 631 MR0089367
36 H Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962) 331 MR0137127
37 W He, S Sun, Frankel conjecture and Sasaki geometry, Adv. Math. 291 (2016) 912 MR3459033
38 S Ishii, Introduction to singularities, Springer (2014) MR3288750
39 K Iwasawa, On some types of topological groups, Ann. of Math. 50 (1949) 507 MR0029911
40 S Kobayashi, Transformation groups in differential geometry, 70, Springer (1972) MR0355886
41 J Kollár, Lectures on resolution of singularities, 166, Princeton Univ. Press (2007) MR2289519
42 B Kotschwar, Kählerity of shrinking gradient Ricci solitons asymptotic to Kähler cones, J. Geom. Anal. 28 (2018) 2609 MR3833809
43 B Kotschwar, L Wang, Rigidity of asymptotically conical shrinking gradient Ricci solitons, J. Differential Geom. 100 (2015) 55 MR3326574
44 B Kotschwar, L Wang, Isometries of asymptotically conical shrinking Ricci solitons, preprint (2019) arXiv:1901.00044
45 H B Laufer, Normal two-dimensional singularities, 71, Princeton Univ. Press (1971) MR0320365
46 R Lazarsfeld, Positivity in algebraic geometry, I : Classical setting : line bundles and linear series, 48, Springer (2004) MR2095471
47 C Li, On rotationally symmetric Kähler–Ricci solitons, preprint (2010) arXiv:1004.4049
48 M T Lock, J A Viaclovsky, A smörgåsbord of scalar-flat Kähler ALE surfaces, J. Reine Angew. Math. 746 (2019) 171 MR3895629
49 D Martelli, J Sparks, S T Yau, Sasaki–Einstein manifolds and volume minimisation, Comm. Math. Phys. 280 (2008) 611 MR2399609
50 Y Matsushima, Sur la structure du groupe d’homéomorphismes analytiques d’une certaine variété kählérienne, Nagoya Math. J. 11 (1957) 145 MR0094478
51 O Munteanu, J Wang, Holomorphic functions on Kähler–Ricci solitons, J. Lond. Math. Soc. 89 (2014) 817 MR3217651
52 O Munteanu, J Wang, Topology of Kähler Ricci solitons, J. Differential Geom. 100 (2015) 109 MR3326575
53 O Munteanu, J Wang, Conical structure for shrinking Ricci solitons, J. Eur. Math. Soc. 19 (2017) 3377 MR3713043
54 O Munteanu, J Wang, Structure at infinity for shrinking Ricci solitons, Ann. Sci. Éc. Norm. Supér. 52 (2019) 891 MR4038455
55 T Ohsawa, Vanishing theorems on complete Kähler manifolds, Publ. Res. Inst. Math. Sci. 20 (1984) 21 MR0736089
56 P Orlik, P Wagreich, Isolated singularities of algebraic surfaces with C action, Ann. of Math. 93 (1971) 205 MR0284435
57 R S Palais, A global formulation of the Lie theory of transformation groups, 22, Amer. Math. Soc. (1957) MR0121424
58 S Pigola, M Rimoldi, A G Setti, Remarks on noncompact gradient Ricci solitons, Math. Z. 268 (2011) 777 MR2818729
59 H Pinkham, Normal surface singularities with C action, Math. Ann. 227 (1977) 183 MR0432636
60 E Prato, S Wu, Duistermaat–Heckman measures in a noncompact setting, Compositio Math. 94 (1994) 113 MR1302313
61 H Rossi, Vector fields on analytic spaces, Ann. of Math. 78 (1963) 455 MR0162973
62 M Siepmann, Ricci flows of Ricci flat cones, PhD thesis, ETH Zürich (2013)
63 G Tian, X Zhu, Uniqueness of Kähler–Ricci solitons, Acta Math. 184 (2000) 271 MR1768112
64 G Tian, X Zhu, A new holomorphic invariant and uniqueness of Kähler–Ricci solitons, Comment. Math. Helv. 77 (2002) 297 MR1915043
65 S Wu, An integration formula for the square of moment maps of circle actions, Lett. Math. Phys. 29 (1993) 311 MR1257832
66 S Wu, On the instanton complex of holomorphic Morse theory, Comm. Anal. Geom. 11 (2003) 775 MR2015176
67 W Wylie, Complete shrinking Ricci solitons have finite fundamental group, Proc. Amer. Math. Soc. 136 (2008) 1803 MR2373611
68 B Yang, A characterization of noncompact Koiso-type solitons, Internat. J. Math. 23 (2012) 1250054, 13 MR2914656
69 Z H Zhang, On the completeness of gradient Ricci solitons, Proc. Amer. Math. Soc. 137 (2009) 2755 MR2497489