Adiabatic theory for the area-constrained Willmore flow

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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 explicitly construct 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).
I. INTRODUCTION
OriginalsprogEngelsk
Artikelnummer041503
TidsskriftJournal of Mathematical Physics
Vol/bind63
Udgave nummer4
Antal sider19
ISSN0022-2488
DOI
StatusUdgivet - 2022

ID: 304180219