On Conditions for Unrectifiability of a Metric Space

• Autorzy: Piotr Hajłasz , Soheil Malekzadeh
• Języki publikacji: EN

Abstrakty

EN

We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.

Słowa kluczowe

EN

geometric measure theory; unrectifiability; metric spaces; Sard theorem; Carnot-Carathéodoryspaces

Kategorie tematyczne

• 53C17: Sub-Riemannian geometry
• 49Q15: Geometric measure and integration theory, integral and normal currents

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-03-07

zaakceptowano

2014-11-15

online

2014-12-17

Twórcy

autor

Piotr Hajłasz

• Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA

autor

Soheil Malekzadeh

• Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA

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Identyfikatory

DOI

10.1515/agms-2015-0001