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Cao, Huai-Dong (ed.) et al., Differential geometry, Calabi-Yau theory, and general relativity. Lectures given at conferences celebrating the 70th birthday of Shing-Tung Yau at Harvard University, Cambridge, MA, USA, May 2019. Somerville, MA: International Press. Surv. Differ. Geom. 23, 35-87 (2020).

MSC: 32Q20 53B35 60G99

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Lahdili, Abdellah

Conformally Kähler, Einstein-Maxwell metrics and boundedness of the modified Mabuchi functional. (English) Zbl 1461.53053

Int. Math. Res. Not. 2020, No. 22, 8418-8442 (2020).

MSC: 53C55 32Q15 53C18

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Qian, Junqing

Hyperbolic metric, punctured Riemann sphere, and modular functions. (English) Zbl 1461.30103

Trans. Am. Math. Soc. 373, No. 12, 8751-8784 (2020).

MSC: 30F45 32Q20

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Datar, Ved V.; Pingali, Vamsi Pritham

On coupled constant scalar curvature Kähler metrics. (English) Zbl 1455.32001

J. Symplectic Geom. 18, No. 4, 961-994 (2020).

Reviewer: Nicolai K. Smolentsev (Kemerovo)

MSC: 32Q15 53D20 53C55 58D17 58B20

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Tian, Gang; Wang, Feng

On the existence of conic Kähler-Einstein metrics. (English) Zbl 1457.53052

Adv. Math. 375, Article ID 107413, 42 p. (2020).

Reviewer: Man-Chun Lee (Evanston)

MSC: 53C55 53C25 14J45 32Q20

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Dervan, Ruadhaí; Székelyhidi, Gábor

The Kähler-Ricci flow and optimal degenerations. (English) Zbl 1447.53081

J. Differ. Geom. 116, No. 1, 187-203 (2020).

MSC: 53E30 14J45 32Q15

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Zhu, Xiaohua

Kähler-Einstein metrics on toric manifolds and \(G\)-manifolds. (English) Zbl 1440.32012

Chen, Jingyi (ed.) et al., Geometric analysis. In honor of Gang Tian’s 60th birthday. Cham: Birkhäuser. Prog. Math. 333, 545-585 (2020).

MSC: 32Q20 14M25 14J45 53E30 32-02

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Rubinstein, Yanir A.

Tian’s properness conjectures: an introduction to Kähler geometry. (English) Zbl 1444.53001

Chen, Jingyi (ed.) et al., Geometric analysis. In honor of Gang Tian’s 60th birthday. Cham: Birkhäuser. Prog. Math. 333, 381-443 (2020).

MSC: 53-01 32-01 53C55 32Q20

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Matsumoto, Yoshihiko

Deformation of Einstein metrics and \(L^2\) cohomology on strictly pseudoconvex domains. (English) Zbl 1443.53030

Trans. Am. Math. Soc. 373, No. 8, 5685-5705 (2020).

MSC: 53C25 32L20 32Q20 32T15 32V05

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Cho, Gunhee; Qian, Junqing

The Kobayashi-Royden metric on punctured spheres. (English) Zbl 1442.32020

Forum Math. 32, No. 4, 911-918 (2020).

MSC: 32F45 32Q45 53C55 32C15 30E15

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Shen, Zhenghan; Zhang, Pan

Canonical metrics on holomorphic filtrations over compact Hermitian manifolds. (English) Zbl 1442.53018

Commun. Math. Stat. 8, No. 2, 219-237 (2020).

MSC: 53C07 53C55 32Q20

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Li, Long; Wang, Jian; Zheng, Kai

Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors. (Métriques singulières coniques avec courbure scalaire prescrite: estimées à priori pour les diviseurs à croisements normaux.) (English. French summary) Zbl 1444.53046

Bull. Soc. Math. Fr. 148, No. 1, 51-97 (2020).

MSC: 53C55 32Q15 32Q20 35B45 53C07 58E15 53D20 14L24

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Chen, Youmin

On expansions of Ricci flat ALE metrics in harmonic coordinates about the infinity. (English) Zbl 1436.32085

Commun. Math. Stat. 8, No. 1, 63-90 (2020).

MSC: 32Q20 53C07 53C21

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Arizmendi, Gerardo; Herrera, Rafael; Piccinni, Paolo

An even Clifford diamond. (English) Zbl 1452.53043

Ann. Global Anal. Geom. 57, No. 3, 465-487 (2020).

Reviewer: Yun Myung Oh (Berrien Springs)

MSC: 53C25 53C15

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Aazami, Amir Babak; Maschler, Gideon

Canonical Kähler metrics on classes of Lorentzian 4-manifolds. (English) Zbl 1443.53041

Ann. Global Anal. Geom. 57, No. 1, 175-204 (2020).

Reviewer: Marcos Origlia (Kortrijk)

MSC: 53C55 53C50 32Q20

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Alekseevsky, Dmitri; Zuddas, Fabio

Cohomogeneity one Kähler and Kähler-Einstein manifolds with one singular orbit. II. (English) Zbl 1433.53097

Ann. Global Anal. Geom. 57, No. 1, 153-174 (2020).

Reviewer: Nicolai K. Smolentsev (Kemerovo)

MSC: 53C55 32Q20 32Q15

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Guenancia, Henri

Families of conic Kähler-Einstein metrics. (English) Zbl 1439.32067

Math. Ann. 376, No. 1-2, 1-37 (2020).

MSC: 32Q20 32Q15

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Zhang, Zhenlei

Openness theorem of conic Kähler-Einstein metrics. (Chinese. English summary) Zbl 1499.53130

Sci. Sin., Math. 49, No. 1, 1-10 (2019).

MSC: 53C07 53C25 53C55

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Nakagawa, Yasuhiro

Kähler-Ricci solitons on certain toric bundles. (English) Zbl 1444.32024

Kyushu J. Math. 73, No. 2, 379-390 (2019).

MSC: 32Q20 14M25 53C55 53C25

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Spotti, Cristiano

Kähler-Einstein metrics via moduli continuity method. (English) Zbl 1457.32060

Codogni, Giulio (ed.) et al., Moduli of \(K\)-stable varieties. Selected papers based on the presentations at the workshop, Rome, Italy, July 10–14, 2017. Cham: Springer. Springer INdAM Ser. 31, 141-152 (2019).

Reviewer: Pengfei Huang (Nice)

MSC: 32Q20 14F45

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Urakawa, Hajime

Biharmonic Hermitian vector bundles over compact Kähler manifolds and compact Einstein Riemannian manifolds. (English) Zbl 1433.53095

Note Mat. 39, No. 2, 95-110 (2019).

MSC: 53C43 58E20 53C07

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Li, Chi; Tian, Gang

Orbifold regularity of weak Kähler-Einstein metrics. (English) Zbl 1431.53077

Rubinstein, Yanir A. (ed.) et al., Advances in complex geometry. Contributions from the JHU-UMD complex geometry seminar, John Hopkins University, Baltimore, MD, USA and University of Maryland, College Park, MD, USA, 2015–2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 735, 169-178 (2019).

MSC: 53C55 53C25 32W20 14E15 32Q30

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Darvas, Tamás

Geometric pluripotential theory on Kähler manifolds. (English) Zbl 1439.32061

MSC: 32Q15 32Q20 32W20

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Fu, Jixiang

Limiting behavior of a class of Hermitian Yang-Mills metrics. I. (English) Zbl 1427.53025

Sci. China, Math. 62, No. 11, 2155-2194 (2019).

MSC: 53C07 32Q20

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Boucksom, Sébastien; Hisamoto, Tomoyuki; Jonsson, Mattias

Uniform K-stability and asymptotics of energy functionals in Kähler geometry. (English) Zbl 1478.53115

J. Eur. Math. Soc. (JEMS) 21, No. 9, 2905-2944 (2019); erratum ibid. 24, No. 2, 735-736 (2022).

MSC: 53C55 14L24 32P05 32Q20 32Q26

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Liu, Yuchen; Xu, Chenyang

\(K\)-stability of cubic threefolds. (English) Zbl 1436.14085

Duke Math. J. 168, No. 11, 2029-2073 (2019).

Reviewer: Andreas Höring (Nice)

MSC: 14L24 14J70

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Zhu, Xiaohua

A brief survey on complex geometry. (Chinese. English summary) Zbl 1438.32030

Adv. Math., Beijing 48, No. 2, 129-136 (2019).

MSC: 32Q99 51M99

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Greb, Daniel; Guenancia, Henri; Kebekus, Stefan

\(\mathrm{klt}\) varieties with trivial canonical class: holonomy, differential forms, and fundamental groups. (English) Zbl 1423.14110

Geom. Topol. 23, No. 4, 2051-2124 (2019).

Reviewer: Juanyong Wang (Palaiseau)

MSC: 14E30 14J32 32J27

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Gontard, Sébastien

On the Kähler-Einstein metric at strictly pseudoconvex points. (English) Zbl 1442.32032

Complex Var. Elliptic Equ. 64, No. 10, 1773-1795 (2019).

Reviewer: Antonella Nannicini (Firenze)

MSC: 32Q20 32T15 53C25

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Stibitz, Charlie; Zhuang, Ziquan

K-stability of birationally superrigid Fano varieties. (English) Zbl 1425.14035

Compos. Math. 155, No. 9, 1845-1852 (2019).

Reviewer: Ilya Karzhemanov (Moscow)

MSC: 14J45 14E05 32Q20

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Li, Chi; Wang, Xiaowei; Xu, Chenyang

On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties. (English) Zbl 1469.14087

Duke Math. J. 168, No. 8, 1387-1459 (2019).

Reviewer: Jingzhou Sun (Shantou)

MSC: 14J45 14J10 14D20 53C55 53C25

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Hashimoto, Yoshinori

Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisor. (La courbure scalaire et l’invariant de Futaki des métriques kählériennes avec des singularités coniques le long d’un diviseur.) (English. French summary) Zbl 1423.53087

Ann. Inst. Fourier 69, No. 2, 591-652 (2019).

Reviewer: Nicoleta Aldea (Brasov)

MSC: 53C55 53C25 32Q20

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Cheltsov, Ivan A.; Rubinstein, Yanir A.; Zhang, Kewei

Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces. (English) Zbl 1418.32015

Sel. Math., New Ser. 25, No. 2, Paper No. 34, 36 p. (2019).

MSC: 32Q20 14J45 32Q15 32Q26

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Futaki, Akito; Ono, Hajime

Conformally Einstein-Maxwell Kähler metrics and structure of the automorphism group. (English) Zbl 1429.32027

Math. Z. 292, No. 1-2, 571-589 (2019).

Reviewer: Andrew Bucki (Edmond)

MSC: 32J27 53C55 32Q15 53C25

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Found 428 Documents (Results 1–100)

Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one. (English) Zbl 07729233

Anticanonically balanced metrics and the Hilbert-Mumford criterion for the \(\delta_m\)-invariant of Fujita-Odaka. (English) Zbl 07720784

Calabi type functionals for coupled Kähler-Einstein metrics. (English) Zbl 07720783

Families of singular Kähler-Einstein metrics. (English) Zbl 07714622

D3-brane supergravity solutions from Ricci-flat metrics on canonical bundles of Kähler-Einstein surfaces. (English) Zbl 07709704

Holomorphic isometries into homogeneous bounded domains. (English) Zbl 07702404

On holomorphic isometries into blow-ups of \(\mathbb{C}^n\). (English) Zbl 1517.53050

The Schwarz lemma in Kähler and non-Kähler geometry. (English) Zbl 1517.32064

Uniform K-stability of polarized spherical varieties. (English) Zbl 07694983

Constant scalar curvature Kähler metrics on ramified Galois coverings. (English) Zbl 07691723

Collapsing Calabi-Yau fibrations and uniform diameter bounds. (English) Zbl 1517.32070

On relations between Mabuchi’s generalized Kähler-Einstein metrics and various canonical Kähler metrics. (English) Zbl 1514.53092

Globally conformally Kähler Einstein metrics on certain holomorphic bundles. (English) Zbl 1517.32069

Moment polytopes on Sasaki manifolds and volume minimization. (English) Zbl 07674742

Variation of singular Kähler-Einstein metrics: Kodaira dimension zero (with an appendix by Valentino Tosatti). (English) Zbl 1511.14053

Some pseudo-Kähler Einstein 4-symmetric spaces with a “twin” special almost complex structure. (English) Zbl 1515.53056

Smooth approximation of twisted Kähler-Einstein metrics. (English) Zbl 1510.32038

Continuity of singular Kähler-Einstein potentials. (English) Zbl 1515.32017

Maxwell-Einstein metrics on completions of certain \(\mathrm{C}^\ast\) bundles. (English) Zbl 1513.53097

Calabi-Yau metrics with cone singularities along intersecting complex lines: the unstable case. (English) Zbl 07730465

Longtime existence of Kähler-Ricci flow and holomorphic sectional curvature. (English) Zbl 07691221

Quasi-Einstein metrics on sphere bundles. (English) Zbl 1507.53049

K-stability of Gorenstein Fano group compactifications with rank two. (English) Zbl 1508.14060

Orbifold stability and Miyaoka-Yau inequality for minimal pairs. (English) Zbl 1505.14035

Kähler-Einstein metrics with prescribed singularities on Fano manifolds. (English) Zbl 1510.32059

Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric. (English) Zbl 1510.32057

The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties. (English) Zbl 1504.32068

Polystable log Calabi-Yau varieties and gravitational instantons. (English) Zbl 1498.14108

Examples of K-unstable Fano manifolds. (Exemples de variétés de Fano K-instables.) (English. French summary) Zbl 1503.14047

Continuity of Monge-Ampère potentials in big cohomology classes. (English) Zbl 1496.32059

Subelliptic estimates from Gromov hyperbolicity. (English) Zbl 1498.32005

Canonical metrics on generalized Hartogs triangles. (English) Zbl 1487.32127

Complete Kähler-Einstein metric on Stein manifolds with negative curvature. (English) Zbl 1487.32143

Erratum to: “Uniform K-stability and asymptotics of energy functionals in Kähler geometry”. (English) Zbl 1483.53087

Twisting non-shearing congruences of null geodesics, almost CR structures and Einstein metrics in even dimensions. (English) Zbl 1491.53077

Relative Ding stability and an obstruction to the existence of Mabuchi solitons. (English) Zbl 1487.32140

The inverse Monge-Ampère flow and applications to Kähler-Einstein metrics. (English) Zbl 1495.32065

Valuative invariants with higher moments. (English) Zbl 1484.32042

Ricci iteration for coupled Kähler-Einstein metrics. (English) Zbl 1487.37045

Existence of canonical metrics in non-Kähler geometry. (English) Zbl 1478.32082

Semi-stability for bi-holomorphic pairs over compact bi-Hermitian Gauduchon manifolds. (English) Zbl 1481.53034

Variation of singular Kähler-Einstein metrics: positive Kodaira dimension. (English) Zbl 1486.32010

Second Ricci flow on noncompact Hermitian manifolds. (English) Zbl 1498.53091

Deformation for coupled Kähler-Einstein metrics. (English) Zbl 1478.32080

Kähler immersions of Kähler-Ricci solitons into definite or indefinite complex space forms. (English) Zbl 1483.53077

On the completeness of some Bianchi type a and related Kähler-Einstein metrics. (English) Zbl 1478.53118

A polar dual to the momentum of toric Fano manifolds. (English) Zbl 1468.14089

Compact Hermitian symmetric spaces, coadjoint orbits, and the dynamical stability of the Ricci flow. (English) Zbl 1471.32034

Gravitating vortices with positive curvature. (English) Zbl 1471.53021

Coupled Sasaki-Ricci solitons. (English) Zbl 1471.53060

Residue formula for an obstruction to coupled Kähler-Einstein metrics. (English) Zbl 1470.32061

Applications of the moduli continuity method to log K-stable pairs. (English) Zbl 1470.32066

Extension of the curvature form of the relative canonical line bundle on families of Calabi-Yau manifolds and applications. (Extension de la forme de courbure du faisceau canonique relatif sur les familles de variétés de Calabi-Yau et applications.) (English. French summary) Zbl 1470.32069

Twisted Kähler-Einstein metrics. (English) Zbl 1470.32067

Tian’s \(\alpha_{m,k}^{\hat{K}}\)-invariants on group compactifications. (English) Zbl 1467.53076

The Bogomolov-Beauville-Yau decomposition for klt projective varieties with trivial first Chern class – without tears. (La décomposition de Bogomolov-Beauville-Yau des variétés projectives klt à première classe de Chern triviale – sans larmes.) (English. French summary) Zbl 1468.14075

Local description of Bochner-flat (pseudo-)Kähler metrics. (English) Zbl 1466.53025

Ricci-flat metrics and dynamics on \(K3\) surfaces. (English) Zbl 1464.14042

Holomorphic families of strongly pseudoconvex domains in a Kähler manifold. (English) Zbl 1460.32051

Invariant metrics on the complex ellipsoid. (English) Zbl 1460.32013

Cheeger-Colding-Tian theory for conic Kähler-Einstein metrics. (English) Zbl 1467.32010

\(G\)-Sasaki manifolds and K-energy. (English) Zbl 1461.53035

Test configurations, stabilities and canonical Kähler metrics. Complex geometry by the energy method. (English) Zbl 1478.32051

Tian’s partial \(C^0\)-estimate implies Hamilton-Tian’s conjecture. (English) Zbl 1479.53105

Bergman-Einstein metrics, a generalization of Kerner’s theorem and Stein spaces with spherical boundaries. (English) Zbl 1462.32039

Weil-Petersson metrics on deformation spaces. (English) Zbl 07649368

An invitation to Kähler-Einstein metrics and random point processes. (English) Zbl 1470.32064

Conformally Kähler, Einstein-Maxwell metrics and boundedness of the modified Mabuchi functional. (English) Zbl 1461.53053

Hyperbolic metric, punctured Riemann sphere, and modular functions. (English) Zbl 1461.30103

On coupled constant scalar curvature Kähler metrics. (English) Zbl 1455.32001

On the existence of conic Kähler-Einstein metrics. (English) Zbl 1457.53052

The Kähler-Ricci flow and optimal degenerations. (English) Zbl 1447.53081

Kähler-Einstein metrics on toric manifolds and \(G\)-manifolds. (English) Zbl 1440.32012

Tian’s properness conjectures: an introduction to Kähler geometry. (English) Zbl 1444.53001

Deformation of Einstein metrics and \(L^2\) cohomology on strictly pseudoconvex domains. (English) Zbl 1443.53030

The Kobayashi-Royden metric on punctured spheres. (English) Zbl 1442.32020