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The Meyers-Serrin theorem on Riemannian manifolds: a survey

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arxiv 2405.13322 v2 pith:VMCEIC53 submitted 2024-05-22 math.AP math.DG

Chi Hin Chan , Magdalena Czubak This is my paper · ORCID
classification math.APmath.DG
keywords derivativesmanifoldsriemannianweakcarefullycovariantdensitydifferential
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We revisit the questions of density of smooth functions, and differential forms, in Sobolev spaces on Riemannian manifolds. We carefully show equivalence of weak covariant derivatives to weak partial derivatives.

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  1. Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds

    math.AP 2024-12 conditional novelty 7.0 of 10

    For rotationally symmetric interactions on high-dimensional spheres, the paper characterizes bifurcation branches and proves a sufficient condition for a discontinuous phase transition.

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