JournalsjemsVol. 22, No. 10pp. 3223–3262

"Bubbling" of the prescribed curvature flow on the torus

  • Michael Struwe

    ETH Zürich, Switzerland
"Bubbling" of the prescribed curvature flow on the torus cover

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Abstract

By a classical result of Kazdan–Warner, for any smooth sign-changing function ff with negative mean on the torus (M,gb)(M,g_b) there exists a conformal metric g=e2ugbg=e^{2u}g_b with Gauss curvature Kg=fK_g=f, which can be obtained from a minimizer uu 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.

Cite this article

Michael Struwe, "Bubbling" of the prescribed curvature flow on the torus. J. Eur. Math. Soc. 22 (2020), no. 10, pp. 3223–3262

DOI 10.4171/JEMS/985