Survey on conformal metrics withrescribed Gaussian curvature n compact Riemannian manifold

有關黎曼曲面上，在給定高斯曲率後，是否存在保角變換，使得原來的黎曼度量跟後來的黎曼度量有這樣的保角關係，若否，是否能找的條件使其成立。If g is a metric on M and if K'' satisfies the sign conditions, is K'' the curvaturef some metric g'', that is pointwise conformal to g.0 Introduction 1 Case of (M) < 0p2 Case of (M)=0p6 Case of (M) > 0 10 Appendix 14.1 Identity in x(M) = 0 14.2 The best constant of Trudinger’s inequality . . . . . . . . . . . 14 Remark on Kazdan-Warner’s work 2