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Convex Programs for Minimal-Area Problems
Name
220_2020_3732_ReferencePDF.pdf
Size
14.95 MB
Format
Adobe PDF
Checksum (MD5)
1bf6953a9862cd097b156616831806b3
Author(s)
Headrick, Matthew
Zwiebach, Barton
Date Issued
March 31, 2020
Publisher
Springer Berlin Heidelberg
Version
Author's final manuscript
Abstract
Abstract
The minimal-area problem that defines string diagrams in closed string field theory asks for the metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least
$$2\pi $$
2
π
. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. We consider the analogous minimal-area problem for homology classes of curves and, with the aid of calibrations and the max flow-min cut theorem, formulate it as a local convex program. We derive an equivalent dual program involving maximization of a concave functional. These two programs give new insights into the form of the minimal-area metric and are amenable to numerical solution. We explain how the homology problem can be modified to provide the solution to the original homotopy problem.
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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00220-020-03732-1
