科研之友
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摘要
On a Riemann surface (Sigma)over bar with smooth boundary, we consider Riemannian metrics conformal to a given background metric. Let kappa be a smooth, positive function on vertical bar K vertical bar/(K). If K denotes the Gauss curvature, then the L (a)-norm of K/kappa 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|/kappa 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.
- 出版日期2012-2
