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The inverse map satisfies $|\phi^{-1}(z)-\phi^{-1}(a)|\leq c|z-a|^{n/(n-2)}$ at any vertex $a$ (reciprocal to the exponent of the direct map). Since this the exponent is $>1$ the inverse is just Lipschitz everywhere. You do not need any general theorems for this. At the vertex the inverse map behaves like a power. At all other points it is smooth (analytic).

The inverse map satisfies $|\phi^{-1}(z)-\phi^{-1}(a)|\leq c|z-a|^{n/(n-2)}$ at any vertex $a$ (reciprocal to the exponent of the direct map). Since this exponent is $>1$ the inverse is just Lipschitz everywhere. You do not need any general theorems for this. At the vertex the inverse map behaves like a power. At all other points it is smooth (analytic).

The inverse map is Hölder with exponent $n/(n-2)$ (reciprocal to the exponent of the direct map). You do not need any general theorems for this. At the vertex the inverse map behaves like a power. At all other points it is smooth (analytic).

The inverse map satisfies $|\phi^{-1}(z)-\phi^{-1}(a)|\leq c|z-a|^{n/(n-2)}$ at any vertex $a$ (reciprocal to the exponent of the direct map). Since this the exponent is $>1$ the inverse is just Lipschitz everywhere. You do not need any general theorems for this. At the vertex the inverse map behaves like a power. At all other points it is smooth (analytic).

The inverse map is Hilder with exponent $n/(n-2)$ (reciprocal to the exponent of the direct map). You do not need any general theorems for this. At the vertex the inverse map behaves like a power. At all other points it is smooth (analytic).

The inverse map is Hölder with exponent $n/(n-2)$ (reciprocal to the exponent of the direct map). You do not need any general theorems for this. At the vertex the inverse map behaves like a power. At all other points it is smooth (analytic).