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UID:news2017@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20260419T161921
DTSTART;TZID=Europe/Zurich:20260423T121500
SUMMARY:Bernoullis Tafelrunde: Mohsen Shahidkalhori (Universität Basel)
DESCRIPTION:Abstract [t3://file?uid=4154]\\r\\nFrequency functions provide 
 a quantitative way to measure how fast a function vanishes. For harmonic m
 aps\, the key fact is that the frequency function is monotone\, and this a
 lready has remarkable consequences: it leads to quantitative unique contin
 uation and prevents solutions from vanishing too rapidly. In particular\, 
 touching sets of harmonic functions are necessarily small\, with codimensi
 on at least two.\\r\\nIn this talk\, we use this viewpoint as a guiding pr
 inciple for more geometric problems. In minimal surface theory\, singulari
 ties arise from sheets touching each other\, suggesting that similar ideas
  should apply. We first examine the linear model given by multi-valued Dir
 ichlet minimizers\, where frequency methods again yield the same dimension
  bounds for the singular set\, and then briefly discuss why extending this
  approach to minimal surfaces is substantially more subtle.
X-ALT-DESC:<p><a href="t3://file?uid=4154">Abstract</a></p>\n<p>Frequency f
 unctions provide a quantitative way to measure how fast a function vanishe
 s. For harmonic maps\, the key fact is that the frequency function is mono
 tone\, and this already has remarkable consequences: it leads to quantitat
 ive unique continuation and prevents solutions from vanishing too rapidly.
  In particular\, touching sets of harmonic functions are necessarily small
 \, with codimension at least two.</p>\n<p>In this talk\, we use this viewp
 oint as a guiding principle for more geometric problems. In minimal surfac
 e theory\, singularities arise from sheets touching each other\, suggestin
 g that similar ideas should apply. We first examine the linear model given
  by multi-valued Dirichlet minimizers\, where frequency methods again yiel
 d the same dimension bounds for the singular set\, and then briefly discus
 s why extending this approach to minimal surfaces is substantially more su
 btle.</p>
DTEND;TZID=Europe/Zurich:20260423T130000
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