Hypergeometric SLE reversibility conjecture

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Let κ∈(0,8)\kappa\in(0,8), let ν>(−4)∨(κ/2−6)\nu>(-4)\vee(\kappa/2-6), and let (Ω;x1,x2,x3,x4)(\Omega;x_1,x_2,x_3,x_4) be a quad. Let η\eta be an hSLE⁡κ(ν)\operatorname{hSLE}_{\kappa}(\nu) in Ω\Omega from x1x_1 to x4x_4 with marked points (x2,x3)(x_2,x_3). Hypergeometric SLE reversibility conjecture. The time-reversal of η\eta has the same law as an hSLE⁡κ(ν)\operatorname{hSLE}_{\kappa}(\nu) in Ω\Omega from x4x_4 to x1x_1 with marked points (x3,x2)(x_3,x_2). The preceding result proves this reversibility for ν≥κ/2−4\nu\geq\kappa/2-4; the conjecture extends it to the full range ν>(−4)∨(κ/2−6)\nu>(-4)\vee(\kappa/2-6).

References

Primary source

Hao Wu, “Hypergeometric SLE: Conformal Markov Characterization and Applications”, arXiv:1703.02022 (2018).

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