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Canonical metrics on generalized Hartogs triangles
Comptes Rendus. Mathématique, 2022 This paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show the existence of a Kähler–Einstein metric on generalized Hartogs triangles.
Bi, Enchao, Hou, Zelin
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Pluricomplex Green's functions and Fano manifolds [PDF]
Épijournal de Géométrie Algébrique, 2019 We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere ...
Nicholas McCleerey, Valentino Tosatti
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Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One
Mathematics, 2021 Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics ...
Jae-Hyouk Lee +2 more
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Smooth approximation of twisted Kähler-Einstein metrics
Advanced Nonlinear Studies, 2023 In this article, we prove the existence of smooth approximations of twisted Kähler-Einstein metrics using the variational method.
Jin Lize, Wang Feng
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K-stability of Fano varieties via admissible flags
Forum of Mathematics, Pi, 2022 We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces ...
Hamid Abban, Ziquan Zhuang
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A polar dual to the momentum of toric Fano manifolds
Complex Manifolds, 2021 We introduce an invariant on the Fano polytope of a toric Fano manifold as a polar dual counterpart to the momentum of its polar dual polytope. Moreover, we prove that if the momentum of the polar dual polytope is equal to zero, then the dual invariant ...
Sano Yuji
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Perelman's entropy for some families of canonical metrics [PDF]
, 2014 We numerically calculate Perelman’s entropy for a variety of canonical metrics on CP1-bundles over products of Fano Kähler-Einstein manifolds. The metrics investigated are Einstein metrics, Kähler-Ricci solitons and quasi-Einstein metrics.
Bérard-Bergery [Bérard-Bergery 82] L. +1 more
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Uniqueness of Kähler-Einstein cone metrics [PDF]
, 2000 The purpose of this paper is to describe a method to construct a Kähler metric with cone singularity along a divisor and to illustrate a type of maximum principle for these incomplete metrics by showing that Kähler-Einstein metrics are unique in ...
Jeffres, Thalia D.
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Kaehler-Einstein Fano threefolds of degree 22 [PDF]
, 2018 We study the problem of existence of Kähler–Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree 22 that admit a faithful action of the multiplicative group C ∗.
Cheltsov, Ivan, Shramov, Constantin
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Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits [PDF]
, 2012 The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones.
Vilcu, Gabriel Eduard, Visinescu, Mihai
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