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SUMMARY:M. B. Karmanova (Sobolev Institute of Mathematics\, Novosibirsk\, 
 Russia)
DTSTART:20250206T110000Z
DTEND:20250206T120000Z
DTSTAMP:20260423T005822Z
UID:mmandim/87
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/87/"
 >Area Formula for Surfaces in Non-Holonomic Structures</a>\nby M. B. Karma
 nova (Sobolev Institute of Mathematics\, Novosibirsk\, Russia) as part of 
 Mathematical models and integration methods\n\n\nAbstract\nNonholonomic st
 ructures can be considered as a natural generalization of the structures o
 f Riemannian geometry. One of their main features is a specific metric\, r
 elative to which one can traverse distances of different orders along diff
 erent directions ($t$\, $t^2$\, $t^3$\, etc.) in time $t$. Therefore\, map
 pings that are Lipschitz in the classical sense are generally not such in 
 the nonholonomic sense\, and vice versa. Nevertheless\, in the second half
  of the 20th century\, the theory of sub-Riemannian differentiability was 
 created\, which allows one to approximate "complicated" mappings by regula
 r ones. Carnot groups are one of the well-known examples of nonholonomic s
 tructures. The talk will discuss the sub-Riemannian analogue of the area f
 ormula for surfaces obtained under intrinsically Lipschitz mappings of ope
 n sets of Carnot groups. Such groups and their generalizations\, Carnot ma
 nifolds\, arise naturally in both theoretical and applied fields\, such as
  neurobiology\, robotics\, and astrodynamics.\n
LOCATION:https://researchseminars.org/talk/mmandim/87/
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