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Conformal welding for critical Liouville quantum gravity

Holden, Nina; Powell, Ellen

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Authors

Nina Holden



Abstract

Consider two critical Liouville quantum gravity surfaces (i.e., γ-LQG for γ = 2), each with the topology of H and with infinite boundary length. We prove that there a.s. exists a conformal welding of the two surfaces, when the boundaries are identified according to quantum boundary length. This results in a critical LQG surface decorated by an independent SLE4. Combined with the proof of uniqueness for such a welding, recently established by McEnteggart, Miller, and Qian (2018), this shows that the welding operation is well-defined. Our result is a critical analogue of Sheffield’s quantum gravity zipper theorem (2016), which shows that a similar conformal welding for subcritical LQG (i.e., γ-LQG for γ ∈ (0, 2)) is well-defined.

Citation

Holden, N., & Powell, E. (2021). Conformal welding for critical Liouville quantum gravity. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 57(3), 1229-1254. https://doi.org/10.1214/20-aihp1116

Journal Article Type Article
Acceptance Date Oct 22, 2020
Online Publication Date Jul 22, 2021
Publication Date 2021-08
Deposit Date Dec 9, 2020
Publicly Available Date Aug 5, 2021
Journal Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Print ISSN 0246-0203
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 57
Issue 3
Pages 1229-1254
DOI https://doi.org/10.1214/20-aihp1116
Related Public URLs https://arxiv.org/abs/1812.11808

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