Moser, R. and Schwetlick, H., 2012. Minimizers of a weighted maximum of the Gauss curvature. Annals of Global Analysis and Geometry, 41 (2), pp. 199-207.
On a Riemann surface [`(S)] with smooth boundary, we consider Riemannian metrics conformal to a given background metric. Let κ be a smooth, positive function on [`(S)]. If K denotes the Gauss curvature, then the L ∞-norm of K/κ gives rise to a functional on the space of all admissible metrics. We study minimizers subject to an area constraint. Under suitable conditions, we construct a minimizer with the property that |K|/κ is constant. The sign of K can change, but this happens only on the nodal set of the solution of a linear partial differential equation.
|Item Type ||Articles|
|Creators||Moser, R.and Schwetlick, H.|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||Moser_AGAG_2011.pdf: The original publication is available at www.springerlink.com|
Actions (login required)