Rafael López-Soriano, David Ruiz
Published 2014-02-10, updated 2014-05-20Version 3
In this paper we study the problem of prescribing the Gaussian curvature under a conformal change of the metric. We are concerned with the problem posed on a subdomain of the 2-sphere under Neumann boundary conditions of the conformal factor. If the area of the subdomain is greater than 2\pi, the associated energy functional is no longer bounded from below. We treat this case by using min-max techniques, giving a new existence result that generalizes and unifies previous work on the argument.
The principal eigenvalue of the $\infty$-Laplacian with the Neumann boundary condition
An indefinite concave-convex equation under a Neumann boundary condition II
A Proof of Hélein's Conjecture on Boundedness of Conformal Factors when n=3
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