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A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundary

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arxiv 0911.3366 v1 pith:A4VXZ2ZC submitted 2009-11-17 math.AP math.DG

YanYan Li , Luc Nguyen This is my paper · ORCID
classification math.APmath.DG
keywords boundaryconformallyflatfullylocallymanifoldsnonlinearproblem
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In this paper we establish existence and compactness of solutions to a general fully nonlinear version of the Yamabe problem on locally conformally flat Riemannian manifolds with umbilic boundary.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The $\sigma_k$-Loewner-Nirenberg problem on Riemannian manifolds for $k=\frac{n}{2}$ and beyond

    math.AP 2025-07 conditional novelty 8.0 of 10

    The fully nonlinear Loewner-Nirenberg problem is shown to admit solutions when mu_Gamma^+>1-delta, in particular for sigma_k with k<=n/2, and whenever any admissible conformal metric exists.

  2. 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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