Polynomial growth harmonic functions on groups of polynomial volume growth
نویسندگان
چکیده
منابع مشابه
Harmonic Functions with Polynomial Growth
Twenty years ago Yau generalized the classical Liouville theo rem of complex analysis to open manifolds with nonnegative Ricci curva ture Speci cally he proved that a positive harmonic function on such a manifold must be constant This theorem of Yau was considerably generalized by Cheng Yau see by means of a gradient estimate which implies the Harnack inequality As a consequence of this gradien...
متن کاملOn polynomial growth functions of D0L-systems
The aim of this paper is to prove that every polynomial function that maps the natural integers to the positive integers is the growth function of some D0L-system.
متن کاملOn Groups whose Geodesic Growth is Polynomial
This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group G has an element whose normal closure is abelian and of finite index, then G has a finite generating set with respect to which the geodesic growt...
متن کاملFinitely generated groups with polynomial index growth
We prove that a finitely generated soluble residually finite group has polynomial index growth if and only if it is a minimax group. We also show that if a finitely generated group with PIG is residually finite-soluble then it is a linear group. These results apply in particular to boundedly generated groups; they imply that every infinite BG residually finite group has an infinite linear quoti...
متن کاملGroups with a Polynomial Dimension Growth
We show that finitely generated groups with a polynomial dimension growth have Yu’s property A and give an example of such groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2015
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-015-1436-5