Let(X,d,μ)be a metric space with a Borel-measureμ,supposeμsatisfies the Ahlfors-regular condition,i.e.birs≤μu(Br(x))≤b2rs,VBr(x)CX,r>0,where bi,b2 are two positive constants and s is the volume growth exponent.I...
the National Natural Science Foundation of China(Grant No.12071047).
This paper is a subsequent work of[Invent.Math.,2013,191:197-253].The second fundamental theorem in Ahlfors covering surface theory is that,for each set E_(q)of q(≥3)distinct points in the extended complex plane C,th...
supported by National Natural Science Foundation of China(Grant No.11531007)。
In the study of the constant in Ahlfors’second fundamental theorem involving a set Eq consisting of q points,branch values of covering surfaces outside Eq bring a lot of troubles.To avoid this situation,for a given s...
National Natural Science Foundation of China (Grant No. 11501259)。
We study the relation between the boundary of a simply connected domainΩbeing Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk...
Supported by National Natural Science Foundation of China (Grant Nos. 10971056 and 10771164)
Let X be an Ahlfors d-regular space and rn a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ(x) ...