可解群上线性增长的调和函数
Harmonic functions of linear growth on solvable groups
摘要：
本文研究了有限维具有固定多项式增长的调和函数空间的非有限生成群的结构。它被证明，这样的群体必须是几乎幂零的（反向克莱纳定理）。我们证明了这确实是可解群的情况。调查的部分动机是克莱纳的证明格罗莫夫定理的群体的多项式增长。
英文摘要：
In this work we study the structure of finitely generated groups for which a space of harmonic functions with fixed polynomial growth is finite dimensional. It is conjectured that such groups must be virtually nilpotent (the converse direction to Kleiner's theorem). We prove that this is indeed the case for solvable groups. The investigation is partly motivated by Kleiner's proof for Gromov's theorem on groups of polynomial growth.
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