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SUMMARY:Volume of the epsilon neighborhood of a submanifold isometrically 
 embedded in R^N
DTSTART:20140520T161500
DTEND:20140520T171500
DTSTAMP:20260916T220422Z
UID:0148d4ab541d11b9ea42dc84e2b311a88e3e9cf8ed8a4b980e9f44e5
CATEGORIES:Conferences - Seminars
DESCRIPTION:Adrien Marcone (EPFL)\nGeometry and Dynamics SeminarAbstract: 
 The talk is concerned with the volume of the epsilon neighbourhood of an i
 sometrically embedded submanifold in R^N. First I will discuss the Steiner
  formula for convex compact subsets of R^n. This formula states that the v
 olume of the epsilon neighbourhood of a convex compact set K in R^N is a p
 olynomial in epsilon whose coefficients are the so-called Quermassintegral
 s of Minkowski.\nAfter that\, I will talk about Weyl's tube formula\, whic
 h is a kind of generalization of the Steiner formula. Weyl proved in 1939 
 that if M is a compact submanifold isometrically embedded in R^N then the 
 volume of the epsilon neighbourhood is also a polynomial in epsilon whose 
 coefficients are called the Lipschitz-Killing curvatures and those only de
 pend on the curvature tensor of M. In particular\, this implies that the v
 olume of this epsilon neighbourhood does not depend on the way the submani
 fold is embedded in the ambiant space.\nThe talk is based on my Master the
 sis.
LOCATION:MA A3 31 http://plan.epfl.ch/?room=MA%20A3%2031
STATUS:CONFIRMED
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