Maximal discs in AdS^{2,1} of Weil-Petersson class parametrize via T^*T_0(1); the Mess map is a symplectic diffeomorphism and anti-holomorphic energy functional is a Kähler potential on T_0(1)^±.
Shen: Weil-Petersson Teichm¨ uller space
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Maximal discs of Weil-Petersson class in $\mathbb{A}\mathrm{d}\mathbb{S}^{2,1}$
Maximal discs in AdS^{2,1} of Weil-Petersson class parametrize via T^*T_0(1); the Mess map is a symplectic diffeomorphism and anti-holomorphic energy functional is a Kähler potential on T_0(1)^±.