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Non-conformal Loewner type estimates for modulus of curve families (2010)
by
Tomasz Adamowicz
,
Nageswari Shanmugalingam
| Citations: | 3 - 1 self |
BibTeX
@MISC{Adamowicz10non-conformalloewner,
author = {Tomasz Adamowicz and Nageswari Shanmugalingam},
title = {Non-conformal Loewner type estimates for modulus of curve families},
year = {2010}
}
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Abstract
We develop various upper and lower estimates for p-modulus of curve families on ring domains in the setting of abstract metric measure spaces and derive p-Loewner type estimates for continua. These estimates are obtained for doubling metric measure spaces or Q-Ahlfors regular metric measure spaces supporting (1, p)-Poincare ́ inequality for the situations of 1 ≤ p ≤ Q and p> Q. We also study p-modulus estimates with respect to Riesz potentials.
