Uniqueness of the critical and supercritical Liouville quantum gravity metrics

Jian Ding; Ewain Gwynne

doi:10.1112/plms.12492

November 10, 2022Proceedings of the London Mathematical SocietyOpen Access

Uniqueness of the critical and supercritical Liouville quantum gravity metrics

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Key Points

To establish the existence and uniqueness of canonical metric spaces associated with Liouville quantum gravity in both critical and supercritical regimes.
Rigorous mathematical analysis and probability theory extending prior metric construction techniques developed for the subcritical regime.
Proof of uniqueness for the Liouville quantum gravity metric in the critical regime corresponding to coupling parameter gamma equals two.
Extension of metric uniqueness results to the supercritical regime beyond the standard subcritical boundary.

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Implication

Theoretical analysis demonstrates the uniqueness of critical and supercritical Liouville quantum gravity metrics, resolving open questions in random geometry.

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Ding et al. (2022) studied this question.

synapsesocial.com/papers/69ff494bda5c1eb07f2d6f98 https://doi.org/10.1112/plms.12492

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Uniqueness of the critical and supercritical Liouville quantum gravity metrics

Key Points

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Implication

Discussion

Cite This Study

Uniqueness of the critical and supercritical Liouville quantum gravity metrics

Key Points

No abstract yet

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Implication

Discussion

Cite This Study

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