光滑度量测度空间上的Liouville型定理
微分几何
2011-01-17 v2
摘要
对于光滑度量测度空间，当Bakry-Emery Ricci张量非负时，我们证明了一个Liouville型定理。这推广了Yau的一个结果，当为常数时即恢复该结果。该结论源于光滑度量测度空间上Bakry-Emery Ricci张量有下界时f-调和函数的梯度估计。
引用
@article{arxiv.1006.0751,
title = {A Liouville-type Theorem for Smooth Metric Measure Spaces},
author = {Kevin Brighton},
journal= {arXiv preprint arXiv:1006.0751},
year = {2011}
}
备注
7 pages. The proofs are modified to remove the assumption that f is bounded. An example is included demonstrating necessity of the remaining assumptions and the exposition is revised to correct typos and increase readability