Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conformal invariants associated with quadratic differentials   Z. Nehari developed a general technique for obtaining inequalities for
conformal maps and domain functions from contour integrals and the Dirichlet
principle. Given a harmonic function with singularity on a domain $R$, it
associates a monotonic functional of subdomains $D \subseteq R$. In the case
that $R$ is conformally equivalent to a disk, we extend Nehari's method by
associating a functional to any quadratic differential on $R$ with specified
singularities. Nehari's method corresponds to the special case that the
quadratic differential is of the form $(\partial q)^2$ for a singular harmonic
function $q$ on $R$. Besides being more general, our formulation is conformally
invariant, and has a particularly elegant equality statement. As an application
we give a one-parameter family of monotonic, conformally invariant functionals
which correspond to growth theorems for bounded univalent functions. These
generalize and interpolate the Pick growth theorems, which appear in a
conformally invariant form equivalent to a two-point distortion theorem of W.
Ma and D. Minda.

27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc