, Volume 38, Issue 2, pp 263-279

Removability theorems for Sobolev functions and quasiconformal maps

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Abstract

We establish several conditions, sufficient for a set to be (quasi)conformally removable, a property important in holomorphic dynamics. This is accomplished by proving removability theorems for Sobolev spaces inR n . The resulting conditions are close to optimal.

The first author is supported by N.S.F. Grant No. DMS-9423746.
The second author is supported by N.S.F. Grants No. DMS-9304580 and DMS-9706875.