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Creators/Authors contains: "Nguyen, Luc"

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  1. ; (, Communications on Pure and Applied Mathematics)
    Abstract For a given finite subsetSof a compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric onM\Ssuch that each point ofScorresponds to an asymptotically flat end and that the Schouten tensor of the conformal metric belongs to the boundary of the given cone. As a by‐product, we define a purely local notion of Ricci lower bounds for continuous metrics that are conformal to smooth metrics and prove a corresponding volume comparison theorem. © 2022 The Authors.Communications on Pure and Applied Mathematicspublished by Wiley Periodicals LLC. 
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  2. ; ; (, Journal of Functional Analysis)
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  3. ; ; (, Proceedings of the London Mathematical Society)
    Abstract We study the regularity of the viscosity solution of the ‐Loewner–Nirenberg problem on a bounded smooth domain for . It was known that is locally Lipschitz in . We prove that, with being the distance function to and sufficiently small, is smooth in and the first derivatives of are Hölder continuous in . Moreover, we identify a boundary invariant which is a polynomial of the principal curvatures of and its covariant derivatives and vanishes if and only if is smooth in . Using a relation between the Schouten tensor of the ambient manifold and the mean curvature of a submanifold and related tools from geometric measure theory, we further prove that, when contains more than one connected components, is not differentiable in . 
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  4. ; ; ; (, Classical and Quantum Gravity)
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