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The Chern-Ricci flow (Q2154796)

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Language	Label	Description	Also known as
English	The Chern-Ricci flow	scientific article

Statements

scholarly article

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The Chern-Ricci flow (English)

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Valentino Tosatti

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Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni

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publication date

15 July 2022

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full work available at URL

https://arxiv.org/abs/2107.12928

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Summary: We give a survey on the Chern-Ricci flow, a parabolic flow of Hermitian metrics on complex manifolds. We emphasize open problems and new directions.

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zbMATH Keywords

Chern-Ricci flow

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Hermitian metrics

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geometric evolution equations

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MaRDI profile type

MaRDI publication profile

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Geometric formalities Along the Chern-Ricci flow

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On the classification of three-dimensional compact Kähler manifolds of nonnegative bisectional curvature

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On compact Kähler surfaces

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Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds

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On the complex structure of Kähler manifolds with nonnegative curvature

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A uniformization theorem for complete non-compact Kähler surfaces with positive bisectional curvature

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\(C^{2,\alpha}\) regularities and estimates for nonlinear elliptic and parabolic equations in geometry

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The parabolic Monge-Ampère equation on compact almost Hermitian manifolds

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The Monge-Ampère equation for non-integrable almost complex structures

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Kähler currents and null loci

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The Chern-Ricci flow on primary Hopf surfaces

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Inoue surfaces and the Chern-Ricci flow

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Unification of the Kähler–Ricci and Anomaly flows

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Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons

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On astheno-Kähler metrics

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Kähler-Ricci flow on projective bundles over Kähler-Einstein manifolds

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The collapsing rate of the Kähler-Ricci flow with regular infinite time singularity

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Generalized Ricci Flow

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Fibrés hermitiens à endomorphisme de Ricci non négatif

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La 1-forme de torsion d'une variété hermitienne compacte

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Locally conformally Kähler metrics on Hopf surfaces

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Convergence of the parabolic complex Monge-Ampère equation on compact Hermitian manifolds

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Collapsing of products along the Kähler-Ricci flow

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The behavior of the Chern scalar curvature under the Chern-Ricci flow

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Complex Monge-Ampère equations and totally real submanifolds

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Geometric Convergence of the Kähler–Ricci Flow on Complex Surfaces of General Type

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Three-manifolds with positive Ricci curvature

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Remarks on the collapsing of torus fibered Calabi–Yau manifolds

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Instantaneously complete Chern-Ricci flow and Kähler-Einstein metrics

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On surfaces of class VII\(_0\)

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On the \(C^\alpha\)-convergence of the solution of the Chern-Ricci flow on elliptic surfaces

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Almost Hermitian Ricci flow

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A continuity method to construct canonical metrics

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Curvature flows for almost-hermitian Lie groups

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On the Chern-Ricci flow and its solitons for Lie groups

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Hermitian manifolds with quasi-negative curvature

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Chern-Ricci flows on noncompact complex manifolds

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Kähler manifolds with almost nonnegative curvature

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The continuity equation of almost Hermitian metrics

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On projectively flat Hermitian manifolds

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On Yau's uniformization conjecture

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GEOMETRY OF HERMITIAN MANIFOLDS

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Comparison geometry of holomorphic bisectional curvature for Kähler manifolds and limit spaces

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An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties

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The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature

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The complex Monge-Ampère type equation on compact Hermitian manifolds and applications

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Ancient solutions to Kähler-Ricci flow

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Regularity of a complex Monge-Ampère equation on Hermitian manifolds

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Weak solutions of the Chern-Ricci flow on compact complex surfaces

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Non-Kähler compact complex manifolds associated to number fields.

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New curvature flows in complex geometry

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Fully non-linear parabolic equations on compact Hermitian manifolds

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The Picard group of a quasi-bundle

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BOUNDING SCALAR CURVATURE AND DIAMETER ALONG THE KÄHLER RICCI FLOW (AFTER PERELMAN)

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Estimates for metrics of constant Chern scalar curvature

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A Chern-Calabi flow on Hermitian manifolds

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Interior derivative estimates for the Kähler-Ricci flow

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Local Calabi and curvature estimates for the Chern-Ricci flow

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The continuity equation, Hermitian metrics and elliptic bundles

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Deforming the metric on complete Riemannian manifolds

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Ricci flow and the uniformization on complete noncompact Kähler manifolds

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The Kähler–Ricci Flow on Projective Bundles

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The Kähler-Ricci flow on surfaces of positive Kodaira dimension

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Canonical measures and Kähler-Ricci flow

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The Kähler-Ricci flow through singularities

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The Kähler–Ricci flow on Hirzebruch surfaces

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Contracting exceptional divisors by the Kähler-Ricci flow

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An Introduction to the Kähler–Ricci Flow

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Contracting exceptional divisors by the Kähler-Ricci flow II

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Pluriclosed Flow and the Geometrization of Complex Surfaces

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A Parabolic Flow of Pluriclosed Metrics

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Hermitian curvature flow

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Gauduchon metrics with prescribed volume form

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Donaldson theory on non-Kählerian surfaces and class VII surfaces with \(b_2=1\)

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Instantons and curves on class VII surfaces

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Non-Kählerian compact complex surfaces

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PROJECTIVELY FLAT SURFACES AND BOGOMOLOV'S THEOREM ON CLASS <font>VII</font><sub>0</sub> SURFACES

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On the Kähler-Ricci flow on projective manifolds of general type

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Convergence of Kähler–Ricci Flow on Lower-Dimensional Algebraic Manifolds of General Type

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Regularizing properties of complex Monge-Ampère flows. II: Hermitian manifolds

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KAWA lecture notes on the K\"ahler-Ricci flow

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The complex Monge-Ampère equation on compact Hermitian manifolds

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The Chern–Ricci flow on complex surfaces

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On the evolution of a Hermitian metric by its Chern-Ricci form

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Collapsing of the Chern-Ricci flow on elliptic surfaces

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Infinite-time singularities of the Kähler-Ricci flow

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Existence and degeneration of Kähler-Einstein metrics on minimal algebraic varieties of general ype

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The Hermitian curvature flow on manifolds with non-negative Griffiths curvature

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On Hermitian curvature flow on almost complex manifolds

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Geometric structures on compact complex analytic surfaces

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The local entropy along Ricci flow part A: the no-local-collapsing theorems

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The Chern-Ricci flow and holomorphic bisectional curvature

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A General Schwarz Lemma for Kahler Manifolds

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On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

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Scalar curvature behavior for finite-time singularity of Kähler-Ricci flow

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The Chern–Ricci Flow on Oeljeklaus–Toma Manifolds

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An almost complex Chern-Ricci flow

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A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics

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The continuity equation of the Gauduchon metrics

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Identifiers

zbMATH Open document ID

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10.4171/RLM/965

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

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