“Large” conformal metrics of prescribed Gauss curvature on surfaces of higher genus

  • Franziska Borer

    ETH Zürich, Switzerland
  • Luca Galimberti

    ETH Zürich, Switzerland
  • Michael Struwe

    ETH Zürich, Switzerland

Abstract

Let be a closed Riemann surface of genus and let be a smooth, non-constant function with , all of whose maximum points are non-degenerate. As shown in [12] for sufficiently small there exist at least two distinct conformal metrics , of Gauss curvature , where is a relative minimizer of the associated variational integral and where is a further critical point not of minimum type. Here, by means of a more refined mountain-pass technique we obtain additional estimates for the "large" solutions that allow to characterize their "bubbling behavior" as .

Cite this article

Franziska Borer, Luca Galimberti, Michael Struwe, “Large” conformal metrics of prescribed Gauss curvature on surfaces of higher genus. Comment. Math. Helv. 90 (2015), no. 2, pp. 407–428

DOI 10.4171/CMH/358