Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adiabatic theory for the area-constrained Willmore flow   In this paper, we develop an adiabatic theory for the evolution of large
closed surfaces under the area-constrained Willmore (ACW) flow in a
three-dimensional asymptotically Schwarzschild manifold. We construct
explicitly a map, defined on a certain four-dimensional manifold of
barycenters, which characterizes key static and dynamical properties of the ACW
flow. In particular, using this map, we find an explicit four-dimensional
effective dynamics of barycenters, which serves as a uniform asymptotic
approximation for the (infinite-dimensional) ACW flow, so long as the initial
surface satisfies certain mild geometric constraints (which determine the
validity interval). Conversely, given any prescribed flow of barycenters
evolving according to this effective dynamics, we construct a family of
surfaces evolving by the ACW flow, whose barycenters are uniformly close to the
prescribed ones on a large time interval (whose size depends on the geometric
constraints of initial configurations).

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga