Weighted cscK metric (I): a priori estimates

Eleonora Di Nezza; Simon Jubert; Abdellah Lahdili

Weighted cscK metric (I): a priori estimates

Differential Geometry 2024-09-20 v2 Complex Variables

Authors: Eleonora Di Nezza , Simon Jubert , Abdellah Lahdili

Abstract

Let $X$ be a compact K\"ahler manifold. In this paper we study the existence of constant weighted scalar curvature K\"ahler (weighted cscK) metrics on $X$ . More precisely, we establish a priori $C^{k}$ -estimates ( $k\geq 0$ ) for the K\"ahler potential associated with these metrics, thereby extending a result due to Chen and Cheng in the classical cscK setting.

Keywords

kähler metrics differential geometry

Cite

@article{arxiv.2407.09929,
  title  = {Weighted cscK metric (I): a priori estimates},
  author = {Eleonora Di Nezza and Simon Jubert and Abdellah Lahdili},
  journal= {arXiv preprint arXiv:2407.09929},
  year   = {2024}
}

Comments

There was a mistake in Lemma 5.5 and Lemma 5.6 where an important term in the estimates was wrongly neglected. We corrected them. The $C^2$ estimate now holds under the assumption that the weight $\mathrm{v}$ is log-concave

Weighted cscK metric (I): a priori estimates

Abstract

Keywords

Cite

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