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DTSTAMP:20260405T192910Z
SUMMARY:Katrin Leschke: Integrable system methods for minimal surfaces.
DESCRIPTION:Abstract: Minimal surfaces\, that is surfaces with vanishing me
 an curvature\, are amongst the surface classes best studied and understood
 . One of the reasons for this is the fact that a minimal surface in 3-spac
 e is the real part of a holomorphic function into complex 3-space\, and th
 us the classical notions and facts from Complex Analysis can be used in th
 e study of minimal surfaces. On the other hand\, harmonic maps into approp
 riate spaces give rise to integrable systems. In particular\, integrable s
 ystem methods can be used to investigate surfaces given by a harmonicity c
 ondition. For example\, constant mean curvature (CMC) surfaces have harmon
 ic Gauss map and the associated family (for non-vanishing mean curvature) 
 has been used to classify all CMC tori as meromorphic functions on an auxi
 liary Riemann surface given by the associated family\, the spectral curve.
  In this talk\, I will explain how some tools from integrable systems\, i.
 e.\, the associated family and its dressing\, give rise to well-known conc
 epts of minimal surfaces. In particular\, this indicates that results on m
 inimal surfaces may be special cases of a more general integrable system t
 heory for conformal immersions.
URL:https://www.imperial.ac.uk/events/105480/katrin-leschke-integrable-syst
 em-methods-for-minimal-surfaces/
DTSTART;TZID=Europe/London:20141023T140000
DTEND;TZID=Europe/London:20141023T150000
LOCATION:United Kingdom
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