NON-CONFORMAL LOEWNER TYPE ESTIMATES FOR MODULUS OF CURVE FAMILIES

被引：28

作者：

Adamowicz, Tomasz ^{[1
]}

Shanmugalingam, Nageswari ^{[1
]}

机构：

[1] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2010年 / 35卷 / 02期

关键词：

p-modulus of curve family; Loewner type theorem; metric measure spaces; conformal mappings; p-capacity; p-harmonic functions; MAPS;

D O I：

10.5186/aasfm.2010.3538

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：609 / 626

页数：18

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