“bubbling” of the Prescribed Curvature Flow on the Torus
نویسنده
چکیده
Abstract. By a classical result of Kazdan-Warner, for any smooth signchanging function f with negative mean on the torus (M,gb) there exists a conformal metric g = egb Gauss curvature Kg = 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.
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