Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry
Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry
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DOI：
10.1007/s00526-021-02079-2
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发表时间：
2021-04
影响因子：
2.1
通讯作者：
Keita Kunikawa;Y. Sakurai
中科院分区：
文献类型：
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作者：
Keita Kunikawa;Y. Sakurai
研究了调和映射热流沿着古超Ricci流的性质，从Perelman约化几何的观点导出了几个具有受控增长的Liouville定理.对于非正弯曲的目标空间，我们的增长条件是尖锐的。对于正弯曲的目标空间，我们的刘维尔定理即使在静态情况下也是新的（即，对于调和映射）;此外，我们指出，增长条件可以得到改善，几乎在静态情况下尖锐。这填补了崔的刘维尔定理和舍恩-乌伦贝克构造的例子之间的差距。
We study harmonic map heat flow along ancient super Ricci flow, and derive several Liouville theorems with controlled growth from Perelman’s reduced geometric viewpoint. For non-positively curved target spaces, our growth condition is sharp. For positively curved target spaces, our Liouville theorem is new even in the static case (i.e., for harmonic maps); moreover, we point out that the growth condition can be improved, and almost sharp in the static case. This fills the gap between the Liouville theorem of Choi and the example constructed by Schoen–Uhlenbeck.