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On the fully nonlinear Yamabe problem with constant boundary mean curvature. I

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arxiv 2410.09683 v1 pith:GNIASLXU submitted 2024-10-13 math.AP math.DG

BaoZhi Chu , YanYan Li , Zongyuan Li This is my paper · ORCID
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keywords equationsliouville-typeoptimalspaceboundaryconformallyconstantcurvature
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In a recent paper, we established optimal Liouville-type theorems for conformally invariant second-order elliptic equations in the Euclidean space. In this work, we prove an optimal Liouville-type theorem for these equations in the half-Euclidean space.

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  1. The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates

    math.AP 2025-07 conditional novelty 8.0 of 10

    For fully nonlinear Loewner-Nirenberg equations with boundary data w=0, the hyperbolic solution is unique when μ_Γ^+>1, while for μ_Γ^+≤1 all solutions form a one-parameter family depending only on x_n.

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