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- 2016
S2上一类HCMU度量的存在性
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Abstract:
摘要 HCMU度量是紧黎曼面上带奇点的extremal度量.研究它的存在性十分重要.通过研究Chen和Wu(Pacific J Math,2009,240(2):267-288)给出的S2上HCMU度量存在的充分必要条件,证明当S2上至少有(N-1)个鞍点时,一定存在non-CSC HCMU度量,其中N是所有锥奇点的个数.
[1] | Wang G F, Zhu X H. Extremal Hermitian metrics on Riemann surfaces with singularities[J]. Duke Math Journal, 2000, 104(2):181-210.</p> |
[2] | <p> Calabi E. Extremal K?hler metrics[C]//Seminar on Differential Geometry, Ann of Math Stud 102. Princeton:Princeton Univ Press, 1982:259-290. |
[3] | Chen X X. Extremal Hermitian metrics on Riemann surfaces[J]. Calc Var, 1999, 8:191-232. |
[4] | Chen X X. Obstruction to the existence of metric whose curvature has umbilical Hessian in a K-surface[J]. Communications in Analysis and Geometry, 2000, 8(2):267-299. |
[5] | Chen Q, Chen X X, Wu Y Y. The structure of HCMU metric in a K-surface[J]. International Mathematics Research Notices, 2005,16:941-958. |
[6] | Lin C S, Zhu X H. Explicit construction of extremal Hermitian metric with finite conical singularities on <em>S</em><sup>2</sup>[J]. Communications in Analysis and Geometry, 2002, 10(1):177-216. |
[7] | Chen Q, Wu Y Y. Existence and expilicit construction of HCMU metrics on <em>S</em><sup>2</sup> and <em>T<sup>2</sup></em>[J]. Pacific Journal of Mathematics, 2009, 240(2):267-288. |
[8] | Chen X X. Weak limits of Riemannian metrics in surfaces with integral curvature bound[J]. Calc Var, 1998, 6:189-226. |