Diameter of Kähler currents
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Vincent Guedj
und
Ahmed Zeriahi
Abstract
We establish upper bounds on the diameter of compact Kähler manifolds endowed with Kähler metrics whose volume form satisfies an Orlicz integrability condition. Our results extend previous estimates due to Fu–Guo–Song, Y. Li, and Guo–Phong–Song–Sturm. In particular, they do not involve any constraint on the vanishing of the volume form. Moreover, we show that singular Kähler–Einstein currents have finite diameter, provided that their local potentials are Hölder continuous.
Funding source: Agence Nationale de la Recherche
Award Identifier / Grant number: ANR-11-LABX-0040
Funding statement: This work has benefited from state aid managed by the ANR-11-LABX-0040, in connection with the research project HERMETIC, as well as by the ANR projects KARMAPOLIS and PARAPLUI and the Institut Universitaire de France.
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Covariant projective representations of Hilbert–Lie groups
- Solutions of the minimal surface equation and of the Monge–Ampère equation near infinity
- A Lindemann–Weierstrass theorem for 𝐸-functions
- Topology and dynamics of compact plane waves
- Diameter of Kähler currents
- CscK metrics near the canonical class
- On 3-nondegenerate CR manifolds in dimension 7 (I): The transitive case
- The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound
- Hodge–Tate stacks and non-abelian 𝑝-adic Hodge theory of v-perfect complexes on rigid spaces
Artikel in diesem Heft
- Frontmatter
- Covariant projective representations of Hilbert–Lie groups
- Solutions of the minimal surface equation and of the Monge–Ampère equation near infinity
- A Lindemann–Weierstrass theorem for 𝐸-functions
- Topology and dynamics of compact plane waves
- Diameter of Kähler currents
- CscK metrics near the canonical class
- On 3-nondegenerate CR manifolds in dimension 7 (I): The transitive case
- The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound
- Hodge–Tate stacks and non-abelian 𝑝-adic Hodge theory of v-perfect complexes on rigid spaces
