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PRODID:-//Memento EPFL//
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SUMMARY:Highly regular Peano surjections
DTSTART:20100617T131500
DTSTAMP:20260407T043904Z
UID:c2830d85487b6a33cd8f2303b6df3a7de57d4b720295475d8ae2963d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Jeremy Tyson  (Urbana-Champaign and UniBern)\nWe study space f
 illing mappings of high regularity. According to the\nclassical results of
  Peano\, Hahn and Mazurkiewicz\, every compact\,\nconnected and locally co
 nnected metric space is the continuous image of\nthe closed unit interval.
  We prove that every compact geodesic metric\nspace is the image of the cl
 osed unit ball in $R^n$ for each $nge 2$ by a\ncontinuous mapping in the S
 obolev class $W^{1\,n}$. Here we use the notion\nof metric space-valued So
 bolev mapping introduced by Ambrosio (1990) and\nReshetnyak (1997). We als
 o study the space filling problem for Lipschitz\nand Holder mappings. As a
 n application\, we show that the first Heisenberg\ngroup\, equipped with i
 ts Carnot-Caratheodory metric\, is the Lipschitz\nimage of $R^5$.
LOCATION:MA-12
STATUS:CONFIRMED
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