Conformal metrics of the disk with prescribed Gaussian and geodesic curvatures
David Ruiz
Abstract:This paper is concerned with the existence of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures. Being more specific, given nonnegative smooth functions K : D → R and h : ∂D → R, we consider the problem of finding a conformal metric realizing K and h as Gaussian and geodesic curvatures, respectively. This is the natural analogue of the classical Nirenberg problem posed on the disk. As we shall see, both curvatures play a role in the existence of solutions. Indeed we are able to giv… Show more
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