Conformal curvature flows on compact manifold of negative Yamabe constant
Conformal curvature flows on compact manifold of negative Yamabe constant
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DOI：
10.1512/iumj.2018.67.7296
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发表时间：
2018
影响因子：
1.1
通讯作者：
Xuezhang Chen;P. Ho
中科院分区：
文献类型：
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作者：
Xuezhang Chen;P. Ho
抽象的。研究了具有负Yamabe常数的光滑紧致黎曼流形（M，g 0）上与预定曲率问题相关的共形曲率流，包括数量曲率流和共形平均曲率流.利用这类流，我们证明了g 0存在唯一的共形度量，使得其内部的标量曲率或边界上的平均曲率等于任意给定的负光滑函数，部分恢复了Kazdan-Warner，奥宾和Escobar的结果.我们还研究了光滑边界的紧致流形上Yamabe型流的孤子。
Abstract. We study some conformal curvature flows related to prescribed curvature problems on a smooth compact Riemannian manifold (M, g0) with or without boundary, which is of negative (generalized) Yamabe constant, including scalar curvature flow and conformal mean curvature flow. Using such flows, we show that there exists a unique conformal metric of g0 such that its scalar curvature in the interior or mean curvature curvature on the boundary is equal to any prescribed negative smooth function, which partially recovers the results of Kazdan-Warner, Aubin and Escobar. We also study the soliton to some Yamabe-type flow on a compact manifold with smooth boundary.