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SUMMARY:Martin Chuaqui Farrú (Pontificia Universidad Católica de Chile)
DTSTART:20210601T130000Z
DTEND:20210601T140000Z
DTSTAMP:20260422T201411Z
UID:CAvid/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/42/">A
 hlfors’ Schwarzians for curves</a>\nby Martin Chuaqui Farrú (Pontificia
  Universidad Católica de Chile) as part of CAvid: Complex Analysis video 
 seminar\n\nLecture held in N/A.\n\nAbstract\nWe discuss Ahlfors' Schwarzia
 n derivatives for curves in euclidean space introduced some three decades 
 ago. The definitions consider separate generalizations of the real and ima
 ginary part of the classical operator in the complex plane that have impor
 tant invariance properties with respect to the Möbius group in euclidean 
 n-space.  We will describe some of the applications of the real Schwarzian
  to the study of simple curves in n-space\, to knots in 3-space\, as well 
 as to the injectivity of the conformal parametrization of minimal surfaces
  in 3-space. The role of the imaginary Schwarzian will be presented in euc
 lidean 3-space\, highlighting its connection with the osculating sphere\, 
 a new transformation law under the Möbius group\, and theorems on the exi
 stence and uniqueness of parametrized curves with prescribed real and imag
 inary Schwarzians.\n
LOCATION:https://researchseminars.org/talk/CAvid/42/
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