Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local duality in Loewner equations   Among diversity of frameworks and constructions introduced in Loewner Theory
by different authors, one can distinguish two closely related but still
different ways of reasoning, which colloquially may be described as
"increasing" and "decreasing". In this paper we review in short the main types
of (deterministic) Loewner evolution discussed in the literature and describe
in detail the local duality between "increasing" and "decreasing" cases within
the general unifying approach in Loewner Theory proposed recently in [Bracci et
al. to appear in J Reine Angew Math; arXiv:0807.1594v1], [Bracci et al. in Math
Ann 344:947-962, 2009; arXiv:0807.1715v1], [Contreras et al. in Revista
Matem\'atica Iberoamericana 26:975-1012, 2010; arXiv:0902.3116v1]. In
particular, we extend several results of R.O.Bauer [in J Math Anal Appl
302:484-501, 2005; arXiv:math/0306130v1], which deal with the chordal Loewner
evolution, to this general setting. Although the duality is given by a simple
change of the parameter, not all the results for the "decreasing" case can be
obtained by mere translating the corresponding results for the "increasing"
case. In particular, as a byproduct of establishing local duality between
evolution families and their "decreasing" counterparts we obtain a new
characterization of generalized Loewner chains.

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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: eess