Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of $L^q$-dimension and entropy dimension of self-conformal
  measures on Riemannian manifolds   Peres and Solomyak proved that on $\mathbb R^n$, the limits defining the
$L^q$-dimension for any $q\in(0,\infty)\setminus\{1\}$, and the entropy
dimension of a self-conformal measure exist, without assuming any separation
condition. By introducing the notions of heavy maximal packings and partitions,
we prove that on a doubling metric space the $L^q$-dimension,
$q\in(0,\infty)\setminus\{1\}$, is equivalent to the generalized dimension. We
also generalize the result on the existence of the $L^q$-dimension to
self-conformal measures on complete Riemannian manifolds with the doubling
property. In particular, these results hold for complete Riemannian manifolds
with nonnegative Ricci curvature. Moreover, by assuming that the measure is
doubling, we extend the result on the existence of the entropy dimension to
self-conformal measures on complete Riemannian manifolds.

31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org