“Large” conformal metrics of prescribed Gauss curvature on surfaces of higher genus
Franziska Borer
ETH Zürich, SwitzerlandLuca Galimberti
ETH Zürich, SwitzerlandMichael 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