CR Yau finite-generation conjecture for Sasakian manifolds

Let MM be a complete noncompact Sasakian (2n+1)(2n+1)-manifold with nonnegative pseudohermitian bisectional curvature, and let OpCR(M)\mathcal{O}_p^{CR}(M) denote the ring of all CR-holomorphic functions on MM of polynomial growth. CR Yau finite-generation conjecture. The ring OpCR(M)\mathcal{O}_p^{CR}(M) is finitely generated. This is presented as the second CR Yau uniformization conjecture, following the stated dimension estimate for CR-holomorphic functions; no resolution is given in the supplied text.

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Primary source

Shu-Cheng Chang, Yingbo Han, Nan Li and Chien Lin, “Existence of nonconstant CR-holomorphic functions of polynomial growth in Sasakian Manifolds”, arXiv:1909.06513 (2019).

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