Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasisymmetric spheres over Jordan domains   Let $\Omega$ be a planar Jordan domain. We consider double-dome-like surfaces
$\Sigma$ defined by graphs of functions of $dist( \cdot ,\partial \Omega)$ over
$\Omega$. The goal is to find the right conditions on the geometry of the base
$\Omega$ and the growth of the height so that $\Sigma$ is a quasisphere, or
quasisymmetric to $\mathbb{S}^2$. An internal uniform chord-arc condition on
the constant distance sets to $\partial \Omega$, coupled with a mild growth
condition on the height, gives a close-to-sharp answer. Our method also
produces new examples of quasispheres in $\mathbb{R}^n$, for any $n\ge 3$.

25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat