Corpus ID: 236034157

# The Teichm\"uller problem for $L^p$-means of distortion

@inproceedings{Martin2021TheTP,
title={The Teichm\"uller problem for \$L^p\$-means of distortion},
author={Gaven J. Martin and Cong Yao},
year={2021}
}
• Published 2021
• Mathematics
Teichmüller’s problem from 1944 is this: Given x ∈ [0, 1) find and describe the extremal quasiconformal map f : D → D, f |∂D = identity and f(0) = −x ≤ 0. We consider this problem in the setting of minimisers of Lp-mean distortion. The classical result is that there is an extremal map of Teichmüller type with associated holomorphic quadratic differential having a pole of order one at x, if x 6= 0. For the Lp-norm, when p = 1 it is known that there can be no locally quasiconformal minimiser… Expand
1 Citations
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We survey a number of recent developments in geometric analysis as they pertain to the calculus of variations and extremal problems in geometric function theory following the NZMRI lectures given byExpand

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