Curvature integral and lipschitz parametrization in 1-regular metric spaces

Annales Academiae Scientiarum Fennicae Mathematica

Volumn 32, Issue 1, 2007, Pages 99-123

  Hahlomaa, Immo ^a  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Lipschitz parametrization; Menger curvature

Indexed keywords

EID: 42149099330     PISSN: 1239629X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

1. n. - Astérisque 193, 1991.
2. FERRARI, F., B. FRANCHI, and H. PAJOT: The geometric traveling salesman problem in the Heisenberg group. - Preprint.
3. HAHLOMAA, I.: Menger curvature and Lipschitz parametrizations in metric spaces. - Fund. Math. 185, 2005, 143-169.
4. JONES, P. W.: Rectifiable sets and the traveling salesman problem. - Invent. Math. 102, 1990, 1-15.
5. LÉGER, J.-C.: Rectifiability and Menger curvature. - Ann. of Math. 149, 1999, 831-869.
6. 2 Jones quantities. - Comm. Pure Appl. Math. 56, 2003, 1294-1365.
7. MATTILA, P., M. S. MELNIKOV, and J. VERDERA: The Cauchy integral, analytic capacity, and uniform rectifiability. - Ann. of Math. 144, 1996, 127-136.
8. n. - J. London Math. Soc. 46, 1992, 336-348.
9. PAJOT, H.: Sous-ensembles de courbes Ahlfors- régulières et nombres de Jones. - Publ. Mat. 40, 1996, 497-526.
10. PAJOT, H.: Analytic capacity, rectifiability, Menger curvature and the Cauchy integral. - Lecture Notes in Math. 1799, Springer-Verlag, Berlin, 2002.
11. SCHUL, R.: Subset of rectifiable curves in Hubert space and the analyst's TSP. - PhD Thesis, Yale University, 2005.