Affiliation:
1. Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China
Abstract
Suppose thatEandE'denote real Banach spaces with dimension at least 2, thatD≠EandD'≠E'are bounded domains with connected boundaries, thatf:D→D'is anM-QH homeomorphism, and thatD'is uniform. The main aim of this paper is to prove thatfextends to a homeomorphismf¯:D¯→D¯'andf-∣∂Dis bilipschitz if and only iffis bilipschitz inD¯. The answer to some open problems of Väisälä is affirmative under a natural additional condition.
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,Analysis
Cited by
1 articles.
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