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SUMMARY:Sigmundur Gudmundsson (Lund University)
DTSTART:20260603T140000Z
DTEND:20260603T150000Z
DTSTAMP:20260603T022701Z
UID:VSGS/135
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/135/">M
 inimal Submanifolds via Harmonic Morphisms - The Method of Eigenfamilies</
 a>\nby Sigmundur Gudmundsson (Lund University) as part of Virtual seminar 
 on geometry with symmetries\n\n\nAbstract\nHarmonic morphisms $\\phi:(M\,g
 )\\to (N\,h)$ are maps between Riemannian manifolds pulling back locally d
 efined real-valued harmonic functions on $(N\,h)$ to harmonic functions on
  $(M\,g)$.  They are solutions to an over-determined non-linear system of 
 partial differential equations\, heavily depending on the geometry of the 
 manifolds involved.  This means that they are difficult to find and do not
  even exist in simple cases.\n\nIn this lecture we give a brief introducti
 on to the general theory and then focus on the special case when the codom
 ain $(N\,h)$ is the standard Euclidean complex plane $\\mathbb C$.  In tha
 t case a regular fibre $\\phi^{-1}(\\{z_0\\})$ of a harmonic morphism $\\p
 hi:(M\,g)\\to\\mathbb C$ is a minimal submanifold of the domain $(M\,g)$ o
 f codimension two.  This is the primary reason for our interest in this ma
 thematical problem.\n\nWe will introduce our "Method of Eigenfamilies" and
  show how this has proven the existence of solutions to this over-determin
 ed non-linear problem for all the Riemannian symmetric spaces.\n
LOCATION:https://researchseminars.org/talk/VSGS/135/
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