Quasiisometric homeomorphisms and $p$-moduli 
of separating sets

A. L. Golberg

The quasi-invariance of $p$-module is a characteristic property for quasiconformal mappings for $p=n$ and for quasiisometric mappings for $p\ne n$. The theorem provide a condition which is more general than the quasi-invariance. This condition completely characterizes quasiisometric homeomorphisms and can be considered as a new definition.

1. Caraman P. $p$-capacity and $p$-modulus, Symp. Math. 18 (1976), 455--484.

2. John F. On quasi-isometric mappings, I, Comm. Pure Appl. Math. 21 (1968), 77–110.

3. John F. On quasi-isometric mappings, II, Comm. Pure Appl. Math. 22 (1969), 265–278.

4. Gehring F. W. Lipschitz mappings and the $p$-capacity of rings in $n$-space, Advances in the theory of Riemann surfaces, Princeton, University Press, 1971, 175--193.

5. Гольберг А. Л. Об одном характеристическом свойстве плоских квазиизоморфизмов, Докл. АН Украины (1994), № 12, 40–41.

6. Gold'shtein V. M., Reshetnyak Yu. G. Quasiconformal Mappings and Sovolev Spaces, Kluwer Academic Publishers Group, 1990.

7. Hesse J. A $p$-extremal lenght and $p$-capacity, Ark. Mat. 13 (1975), 131--144.

8. Ziemer W. P. Extremal length and $p$-capacity, Michigan Math. J. 16 (1969), 43--51.

	Quasiisometric homeomorphisms and $p$-moduli of separating sets
Author	A. L. Golberg golbera@macs.biu.ac.il Department of Mathematics and Statistics, ,Bar-Ilan University, 52900 Ramat-Gan, Israel
Abstract	The quasi-invariance of $p$-module is a characteristic property for quasiconformal mappings for $p=n$ and for quasiisometric mappings for $p\ne n$. The theorem provide a condition which is more general than the quasi-invariance. This condition completely characterizes quasiisometric homeomorphisms and can be considered as a new definition.
Keywords	quasiisometry, homeomorphism, separating set
DOI	doi:10.30970/ms.21.1.101-104
Reference	1. Caraman P. $p$-capacity and $p$-modulus, Symp. Math. 18 (1976), 455--484. 2. John F. On quasi-isometric mappings, I, Comm. Pure Appl. Math. 21 (1968), 77–110. 3. John F. On quasi-isometric mappings, II, Comm. Pure Appl. Math. 22 (1969), 265–278. 4. Gehring F. W. Lipschitz mappings and the $p$-capacity of rings in $n$-space, Advances in the theory of Riemann surfaces, Princeton, University Press, 1971, 175--193. 5. Гольберг А. Л. Об одном характеристическом свойстве плоских квазиизоморфизмов, Докл. АН Украины (1994), № 12, 40–41. 6. Gold'shtein V. M., Reshetnyak Yu. G. Quasiconformal Mappings and Sovolev Spaces, Kluwer Academic Publishers Group, 1990. 7. Hesse J. A $p$-extremal lenght and $p$-capacity, Ark. Mat. 13 (1975), 131--144. 8. Ziemer W. P. Extremal length and $p$-capacity, Michigan Math. J. 16 (1969), 43--51.
Pages	101-104
Volume	21
Issue	1
Year	2004
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Quasiisometric homeomorphisms and $p$-moduli of separating sets