Some Dirichlet problems arising from conformal geometry
Some Dirichlet problems arising from conformal geometry
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DOI：
10.2140/pjm.2011.251.337
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发表时间：
2011-06
影响因子：
0.6
通讯作者：
Qi-Rui Li;Weimin Sheng
中科院分区：
文献类型：
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作者：
Qi-Rui Li;Weimin Sheng
我们研究了在有边界的紧流形上寻找由修正的Schouten张量的一些对称函数确定的完整共角度量的问题；这简化为狄利克雷问题。我们证明了在一些合适的条件下该解的存在性。特别地，我们证明了每个具有边界的光滑紧致 n 维流形（n ≥ 3）都承认一个完整的黎曼度量 g，其 Ricci 曲率 Ricg 和标量曲率 R g 满足该结果在标量曲率情况下推广了 Aviles 和 McOwen 的结果。
We study the problem of finding complete conformal metrics determined by some symmetric function of the modified Schouten tensor on compact manifolds with boundary; which reduces to a Dirichlet problem. We prove the existence of the solution under some suitable conditions. In particular, we prove that every smooth compact n-dimensional manifold with boundary, with n ≥ 3, admits a complete Riemannian metric g whose Ricci curvature Ricg and scalar curvature R g satisfy This result generalizes Aviles and McOwen's in the scalar curvature case.