View source for Zorich theorem

In 1967, V.A. Zorich proved the following result for [[quasi-regular mapping]]s in space: A [[Local homeomorphism|locally homeomorphic]] quasi-regular mapping $f : \mathbf{R}^n \rightarrow \mathbf{R}^n$, $n \ge 3$, is, in fact, a [[homeomorphism]] of $\mathbf{R}^n$.

This result had been conjectured by M.A. Lavrent'ev in 1938. Note that the exponential function shows that there is no such result for $n=2$. In 1971, O. Martio, S. Rickman and J. Väisälä proved a stronger quantitative result: For $n \ge 3$ and $K > 1$ there exists a number $\psi(n,K) \in (0,1)$ , the ''radius of injectivity'', such that every locally injective $K$-quasi-regular mapping $f : B^n \rightarrow \mathbf{R}^n$, where $B^b = B^n(1)$ and $B^n(r) = \{ x \in \mathbf{R}^n : |x| \le r \}$, for $r > 0$, is injective in $B^n(\psi(n,K))$.

====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  S. Rickman,   "Quasiregular mappings" , ''Ergeb. Math. Grenzgeb.'' , '''26''' , Springer  (1993)</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  V.A. Zorich,   "The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems"  M. Vuorinen (ed.) , ''Quasiconformal Space Mappings'' , ''Lecture Notes in Mathematics'' , '''1508'''  (1992)  pp. 132–148</TD></TR>
<TR><TD valign="top">[a3]</TD> <TD valign="top">  O. Martio,   U. Sebro,   "Universal radius of injectivity for locally quasiconformal mappings"  ''Israel J. Math.'' , '''29'''  (1978)  pp. 17–23</TD></TR>
</table>

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