Research profile

Johannes Schäfer

Works on Kähler–Ricci solitons, Kähler geometry and Ricci-flat & Calabi–Yau.

NP-RC-896338

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Kähler–Ricci solitonsKähler geometryRicci-flat & Calabi–YauRicci solitonsLong-time existence & convergenceStability & uniqueness

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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2021

math.DGv2arXiv:2103.12629

Asymptotically cylindrical steady Kähler-Ricci solitons

Johannes Schäfer

Let be a compact Kähler manifold with trivial canonical bundle and be a finite cyclical group of order acting on by biholomorphisms, where the action on the first factor is generated by rotation of angle . Furthermore, suppose that is a trivialisation of the canonical bundle such that preserves the holomorphic form on , with denoting the coordinate on . The main result of this article is the construction of new examples of gradient steady Kähler-Ricci solitons on certain crepant resolutions of the orbifolds . These new solitons converge exponentially to a Ricci-flat cylinder .

Ricci solitonsKähler–Ricci solitonsRicci-flat & Calabi–YauKähler geometryLong-time existence & convergence
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2020

math.DGv3arXiv:2001.09858

Existence and uniqueness of -invariant Kähler-Ricci solitons

Johannes Schäfer

We use the momentum construction for -invariant Kähler metrics as developed by Hwang-Singer to construct new examples of steady Kähler-Ricci solitons. We also prove that these solitons are unique in their Kähler class, provided the vector field and the asymptotic behaviour are fixed.

Ricci solitonsKähler–Ricci solitonsKähler geometryStability & uniqueness
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