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edit approved Nov 9, 2015 at 19:33
Tadashi
edit approved Nov 9, 2015 at 19:33
Tadashi
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The article "Quasimöbius maps""Quasimöbius maps" by Jussi Väisälä states that one always has the implication QM $\implies$ QC. But a proof is only given in for maps of the form $f:\dot{A} \to \dot{Y}$ where $A \subset \dot{X}$ and where $\dot{X} = X \cup \{\infty\}$ denotes the one-point extension of the metric space $X$.

Does the statement hold for all QM maps between arbitrary metric spaces? Does anyone know a reference to a paper where the relationship between QM and QC for arbitrary metric spaces is shown more clear?

The article "Quasimöbius maps" by Jussi Väisälä states that one always has the implication QM $\implies$ QC. But a proof is only given in for maps of the form $f:\dot{A} \to \dot{Y}$ where $A \subset \dot{X}$ and where $\dot{X} = X \cup \{\infty\}$ denotes the one-point extension of the metric space $X$.

Does the statement hold for all QM maps between arbitrary metric spaces? Does anyone know a reference to a paper where the relationship between QM and QC for arbitrary metric spaces is shown more clear?

The article "Quasimöbius maps" by Jussi Väisälä states that one always has the implication QM $\implies$ QC. But a proof is only given in for maps of the form $f:\dot{A} \to \dot{Y}$ where $A \subset \dot{X}$ and where $\dot{X} = X \cup \{\infty\}$ denotes the one-point extension of the metric space $X$.

Does the statement hold for all QM maps between arbitrary metric spaces? Does anyone know a reference to a paper where the relationship between QM and QC for arbitrary metric spaces is shown more clear?

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CAT0
CAT0
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Are quasi-Möbius maps always quasi-conformal?

The article "Quasimöbius maps" by Jussi Väisälä states that one always has the implication QM $\implies$ QC. But a proof is only given in for maps of the form $f:\dot{A} \to \dot{Y}$ where $A \subset \dot{X}$ and where $\dot{X} = X \cup \{\infty\}$ denotes the one-point extension of the metric space $X$.

Does the statement hold for all QM maps between arbitrary metric spaces? Does anyone know a reference to a paper where the relationship between QM and QC for arbitrary metric spaces is shown more clear?