- Journal Article
By a classical result of Kazdan-Warner, for any smooth sign-changing function f with negative mean on the torus (M, gb) there exists a conformal metric g = e(2u) g(b) with Gauss curvature K-g = f, which can be obtained from a minimizer u of Dirichlet's integral in a suitably chosen class of functions. As shown by Galimberti, these minimizers exhibit "bubbling" in a certain limit regime. Here we sharpen Galimberti's result by showing that all resulting "bubbles" are spherical. Moreover, we prove that analogous "bubbling" occurs in the prescribed curvature flow. Show more
Journal / seriesJournal of the European Mathematical Society
Pages / Article No.
PublisherEuropean Mathematical Society
SubjectPrescribed curvature; conformal geometry; geometric flows; Concentration phenomena
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