Weighted K-stability of polarized varieties and extremality of Sasaki manifolds

Apostolov, 2021, The CR geometry of weighted extremal Kähler and Sasaki metrics, Math. Ann., 379, 1047, 10.1007/s00208-020-02095-1 Apostolov, 2020, Levi–Kähler reduction of CR structures, product of spheres, and toric geometry, Math. Res. Lett., 27, 1565, 10.4310/MRL.2020.v27.n6.a1 Apostolov, 2004, Hamiltonian 2-forms in Kähler geometry, II global classification, J. Differ. Geom., 68, 277, 10.4310/jdg/1115669513 Apostolov, 2008, Hamiltonian 2-forms in Kähler geometry, III extremal metrics and stability, Invent. Math., 173, 547, 10.1007/s00222-008-0126-x Apostolov, 2019, Conformally Kähler, Einstein–Maxwell geometry, J. Eur. Math. Soc., 21, 1319, 10.4171/JEMS/862 Apostolov, 2021, Weighted extremal Kähler metrics and the Einstein–Maxwell geometry of projective bundles, Commun. Anal. Geom. Berman, 2017, Convexity of the K-energy on the space of Kähler metrics and uniqueness of extremal metrics, J. Am. Math. Soc., 30, 1165, 10.1090/jams/880 Berman, 2020, Regularity of weak minimizers of the K-energy and applications to properness and K-stability, Ann. Sci. Éc. Norm. Supér., 53, 267, 10.24033/asens.2422 Berndtsson, 2015, A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry, Invent. Math., 200, 149, 10.1007/s00222-014-0532-1 Boucksom, 2017, Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs, Ann. Inst. Fourier, 67, 743, 10.5802/aif.3096 Boyer, 2008, Sasakian Geometry Boyer, 2008, Canonical Sasakian metrics, Commun. Math. Phys., 279, 705, 10.1007/s00220-008-0429-1 Boyer, 2018, An application of the Duistertmaat–Heckman theorem and its extensions in Sasaki geometry, Geom. Topol., 22, 4205, 10.2140/gt.2018.22.4205 Boyer, 2018, Relative K-stability and extremal Sasaki metrics, Math. Res. Lett., 28, 1, 10.4310/MRL.2018.v25.n1.a1 Calabi, 1982, Extremal Kähler metrics, vol. 102, 259 Chen Cho, 2008, Uniqueness and examples of compact toric Sasaki–Einstein metrics, Commun. Math. Phys., 277, 439, 10.1007/s00220-007-0374-4 Collins, 2018, K-semistability for irregular Sasaki manifolds, J. Differ. Geom., 109, 81, 10.4310/jdg/1525399217 Collins, 2019, Sasaki-Einstein metrics and K-stability, Geom. Topol., 23, 1339, 10.2140/gt.2019.23.1339 Darvas, 2015, The Mabuchi geometry of finite energy class, Adv. Math., 285, 182, 10.1016/j.aim.2015.08.005 Darvas, 2017, Tian's properness conjectures and Finsler geometry of the space of Kähler metrics, J. Am. Math. Soc., 3, 347 David, 2004, Weyl connections and curvature properties of CR manifolds, Ann. Glob. Anal. Geom., 26, 59, 10.1023/B:AGAG.0000023204.71677.bf Dervan, 2017, K-stability for Kähler manifolds, Math. Res. Lett., 24, 689, 10.4310/MRL.2017.v24.n3.a5 Donaldson, 1997, Remarks on gauge theory, complex geometry and 4-manifold topology, vol. 5, 384 Donaldson, 2002, Scalar curvature and stability of toric varieties, J. Differ. Geom., 62, 289, 10.4310/jdg/1090950195 El Kacimi-Alaoui, 1990, Opérateurs transversalement elliptiques sur un feuilletage riemannien et applications, Compos. Math., 73, 57 Falcão, 1997, Moment maps on symplectic cones, Pac. J. Math., 181, 357, 10.2140/pjm.1997.181.357 Futaki, 2019, Conformally Einstein–Maxwell Kähler metrics and structure of the automorphism group, Math. Z., 292, 571, 10.1007/s00209-018-2112-3 Futaki, 2009, Transverse Kähler geometry of Sasaki manifolds and toric Sasaki–Einstein manifolds, J. Differ. Geom., 83, 585, 10.4310/jdg/1264601036 Phong, 2007, Test configurations for K-stability and geodesic rays, J. Symplectic Geom., 5, 221, 10.4310/JSG.2007.v5.n2.a3 Gauduchon, 2014, Calabi's Extremal Metrics: An Elementary Introduction He, 2014, On the transverse scalar curvature of a compact Sasaki manifold, Complex Manifolds, 1, 52, 10.2478/coma-2014-0004 He, 2019, On Calabi's extremal metric and properness, Trans. Am. Math. Soc., 372, 5595, 10.1090/tran/7744 He He, 2021, Geometric pluripotential theory on Sasaki manifolds, J. Geom. Anal., 31, 1093, 10.1007/s12220-019-00257-5 He, 2016, Frankel conjecture and Sasaki geometry, Adv. Math., 291, 912, 10.1016/j.aim.2015.11.053 Lahdili, 2019, Automorphisms and deformations of conformally Kähler, Einstein–Maxwell metrics, J. Geom. Anal., 29, 542, 10.1007/s12220-018-0010-x Lahdili, 2020, Conformally Kähler, Einstein–Maxwell metrics and boundedness of the modified Mabuchi functional, Int. Math. Res. Not., 2020, 8418 Lahdili, 2019, Kähler metrics with weighted constant scalar curvature and weighted K-stability, Proc. Lond. Math. Soc., 119, 1065, 10.1112/plms.12255 Lahdili Legendre, 2011, Existence and non-uniqueness of constant scalar curvature toric Sasaki metrics, Compos. Math., 147, 1613, 10.1112/S0010437X1100529X Lejmi, 2010, Extremal almost-Kähler metrics, Int. J. Math., 21, 1639, 10.1142/S0129167X10006690 Lerman, 2002, A convexity theorem for torus actions on a contact manifold, Ill. J. Math., 46, 171 Li, 2014, Special test configuration and K-stability of Fano varieties, Ann. Math., 180, 197, 10.4007/annals.2014.180.1.4 Li, 2018, Stability of valuations: higher rational rank, Peking Math. J., 1, 1, 10.1007/s42543-018-0001-7 Martelli, 2006, The geometric dual of a-maximisation for toric Sasaki–Einstein manifolds, Commun. Math. Phys., 268, 39, 10.1007/s00220-006-0087-0 Martelli, 2008, Sasaki–Einstein manifolds and volume minimisation, Commun. Math. Phys., 280, 611, 10.1007/s00220-008-0479-4 Odaka, 2013, A generalization of the Ross–Thomas slope theory, Osaka J. Math., 50, 171 Reid, 2002, Graded Rings and Varieties in Weighted Projective Space Ross, 2011, Weighted projective embeddings, stability of orbifolds, and constant scalar curvature Kähler metrics, J. Differ. Geom., 88, 109, 10.4310/jdg/1317758871 Sjöström Dyrefelt, 2018, K-semistability of cscK manifolds with transendental cohomology class, J. Geom. Anal., 28, 2927, 10.1007/s12220-017-9942-9 Sjöström Dyrefelt, 2020, (with an Appendix by R. Dervan), On K-polystability of CSCK manifolds with transcendental cohomology class, Int. Math. Res. Not., 2020, 2769, 10.1093/imrn/rny094 Székelyhidi, 2007, Extremal metrics and K-stability, Bull. Lond. Math. Soc., 39, 76, 10.1112/blms/bdl015 Tian, 1994, The K-energy on hypersurfaces and stability, Commun. Anal. Geom., 2, 239, 10.4310/CAG.1994.v2.n2.a4 Tian, 1997, Kähler–Einstein metrics with positive scalar curvature, Invent. Math., 130, 1, 10.1007/s002220050176 van Coevering, 2013, Stability of Sasaki-extremal metrics under complex deformations, Int. Math. Res. Not., 24, 5527, 10.1093/imrn/rns210 van Coevering van Coevering, 2011, Examples of asymptotically conical Ricci-flat Kähler manifolds, Math. Z., 267, 465, 10.1007/s00209-009-0631-7 Wang, 2012, Height and GIT weight, Math. Res. Lett., 18, 909, 10.4310/MRL.2012.v19.n4.a14 Webster, 1977, On the pseudo-conformal geometry of a Kähler manifold, Math. Z., 157, 265, 10.1007/BF01214356 Yau, 1990, Open problems in geometry, vol. 54, 1 Zhou, 2008, Relative K-stability and modified K-energy on toric manifolds, Adv. Math., 219, 1327, 10.1016/j.aim.2008.06.016