Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz
  Potential   The Schwarz function has played an elegant role in understanding and in
generating new examples of exact solutions to the Laplacian growth (or "Hele-
Shaw") problem in the plane. The guiding principle in this connection is the
fact that "non-physical" singularities in the "oil domain" of the Schwarz
function are stationary, and the "physical" singularities obey simple dynamics.
We give an elementary proof that the same holds in any number of dimensions for
the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17]
(1989). A generalization is also given for the so-called "elliptic growth"
problem by defining a generalized Schwarz potential. New exact solutions are
constructed, and we solve inverse problems of describing the driving
singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n -
techniques can be used to locate the singularity set of the Schwarz potential.
One of our methods is to prolong available local extension theorems by
constructing "globalizing families". We make three conjectures in potential
theory relating to our investigation.

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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
32
The categories of this paper are: atom-ph