Geodesic
Regularizing and self-avoidance effects of integral Menger curvature
Strzelecki, Paweł1 ; Szumańska, Marta2 ; von der Mosel, Heiko3 
1 Instytut Matematyki, Uniwersytet Warszawski, ul. Banacha 2, PL-02-097 Warsaw, Poland
2 Instytut Matematyczny, Polskiej Akademii Nauk, ul. Śniadeckich 8, PL-00-950 Warsaw, Poland
3 Institut für Mathematik, RWTH Aachen University, Templergraben 55, D–52062 Aachen, Germany
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 145-187

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We investigate geometric curvature energies on closed curves involving integral versions of the Menger curvature. In particular, we prove geometric variants of Morrey-Sobolev and Morrey-space imbedding theorems, which may be viewed as counterparts to respective results on one-dimensional sets in the context of harmonic analysis.

Classification : 28A75, 53A04, 46E35

Strzelecki, Paweł 1 ; Szumańska, Marta 2 ; von der Mosel, Heiko 3

1 Instytut Matematyki, Uniwersytet Warszawski, ul. Banacha 2, PL-02-097 Warsaw, Poland
2 Instytut Matematyczny, Polskiej Akademii Nauk, ul. Śniadeckich 8, PL-00-950 Warsaw, Poland
3 Institut für Mathematik, RWTH Aachen University, Templergraben 55, D–52062 Aachen, Germany 
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     title = {Regularizing and self-avoidance effects of integral {Menger} curvature},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {145--187},
     publisher = {Scuola Normale Superiore, Pisa},
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     url = {http://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_1_145_0/}
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Strzelecki, Paweł; Szumańska, Marta; von der Mosel, Heiko. Regularizing and self-avoidance effects of integral Menger curvature. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 145-187. http://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_1_145_0/