Universal radius of injectivity for locally quasiconformal mappings (original) (raw)

Abstract

If n >2 and if [ is a locally quasiconformal mapping from the ball B "= {x • R" :Ix I < 1}into R" U {~}then f is injective in B"(r)= {x ~ R" :Ix I < r}

Key takeaways

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  1. The universal radius of injectivity for quasimeromorphic mappings is established for dimensions n > 3.
  2. Injectivity in B"(r) depends solely on n and the maximal dilatation K(f).
  3. The results for quasimeromorphic mappings extend previous findings for quasiregular mappings.
  4. For n = 2, the injectivity condition does not hold, demonstrated by complex function examples.
  5. The text resolves an open problem regarding the dispensability of the condition fB" C R".

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References (11)

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  11. AND TECHNION--ISRAEL INSTITUTE OF TECHNOLOGY HAIFA, ISRAEL