Is there always an extremal Teichmüller mapping?

Yao, Guowu

doi:10.1007/bf02789054

Cited by 12 publications

(11 citation statements)

References 14 publications

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“…We take f to be the example of extremal quasi-conformal mapping constructed in [12] by Yao, where f is used for showing that [f ] contains no Teichmüller extremal mappings.…”

Section: Remarksmentioning

confidence: 99%

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A note on extremal quasi-conformal mappings

2010

Sci. China Ser. A-Math.

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An extremal quasi-conformal mapping f of a domain D is said to be of non-landslide type if the set E f (δ) := {z ∈ D : |μ f (z)| μ ∞ − δ} has no interior points for any δ > 0. In this paper, we construct a quasi-conformal mapping f of the unit disc D such that its Teichmüller equivalence class [f ] contains infinitely many extremal mappings of non-landslide type. The relation between extremal mappings of non-landslide type and locally extremal mappings is also discussed.Keywords quasi-conformal mappings, extremal quasi-conformal mappings, locally extremal quasi-conformal mappings MSC(2000): Primary 37F30, Secondary 30F70Citation: Li Z. A note on extremal quasi-conformal mappings.

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“…We take f to be the example of extremal quasi-conformal mapping constructed in [12] by Yao, where f is used for showing that [f ] contains no Teichmüller extremal mappings.…”

Section: Remarksmentioning

confidence: 99%

“…Now we briefly introduce the the main idea of the construction of the example in [12] and show how it works for our goal.…”

Section: Remarksmentioning

confidence: 99%

A note on extremal quasi-conformal mappings

2010

Sci. China Ser. A-Math.

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“…Problem 1 [11] . If [μ] T (Δ) contains extremal Teichmüller Beltrami coefficients, does it imply that [μ] B(Δ) contains extremal Teichmüller Beltrami coefficients, and vice versa?…”

Section: Extremal Beltrami Coefficients With Non-constant Modulusmentioning

confidence: 99%

“…Following Theorems 1 and 2, we answer some problems proposed in [11,12] by Yao. In the next section, we introduce the problems.…”

Section: Introductionmentioning

confidence: 95%

On the equivalence of extremal Teichmüller mapping

Fan

Chen

2008

Sci. China Ser. A-Math.

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“…It is known that B(R) is the tangent space of Teichmüller space T (R) at the basepoint. For some basic definitions and notation relating to Teichmüller space, we refer the reader to the books [4,5] and the paper [11].…”

Section: Introductionmentioning

confidence: 99%