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  • 學位論文

黎曼曲面上之保角變換

Survey on conformal metrics with prescribed Gaussian curvature on compact Riemannian manifold

指導教授 : 王藹濃

摘要


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。

關鍵字

保角變換

並列摘要


If g is a metric on M and if K' satisfies the sign conditions, is K' the curvature of some metric g', that is pointwise conformal to g.

參考文獻


[2] L. Kazdan and F. Warner. Curvature function for compact 2-manifold.
[4] X. Xu and P.Yang, Remarks on prescribing Gauss curvture
[1] J.Moser, A sharp Form of an inequality by N.Trudinger. Indiana University
mathematic Journals,vol.20, 1971.
The Annals of Mathematics,second series,vol.99,no.1,p14-47

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