TY - JOUR
T1 - The p-Weil–Petersson Teichmüller Space and the Quasiconformal Extension of Curves
AU - Wei, Huaying
AU - Matsuzaki, Katsuhiko
N1 - Funding Information:
Research supported by Japan Society for the Promotion of Science (KAKENHI 18H01125 and 21F20027)
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/8
Y1 - 2022/8
N2 - We consider the correspondence between the space of p-Weil–Petersson curves γ on the plane and the p-Besov space of u= log γ′ on the real line for p> 1. We prove that the variant of the Beurling–Ahlfors extension defined by using the heat kernel yields a holomorphic map for u on a domain of the p-Besov space to the space of p-integrable Beltrami coefficients. This in particular gives a global real-analytic section for the Teichmüller projection from the space of p-integrable Beltrami coefficients to the p-Weil–Petersson Teichmüller space.
AB - We consider the correspondence between the space of p-Weil–Petersson curves γ on the plane and the p-Besov space of u= log γ′ on the real line for p> 1. We prove that the variant of the Beurling–Ahlfors extension defined by using the heat kernel yields a holomorphic map for u on a domain of the p-Besov space to the space of p-integrable Beltrami coefficients. This in particular gives a global real-analytic section for the Teichmüller projection from the space of p-integrable Beltrami coefficients to the p-Weil–Petersson Teichmüller space.
KW - A-weights
KW - BMO functions
KW - Besov space
KW - Beurling–Ahlfors extension
KW - Global section of Teichmüller projection
KW - Integrable Beltrami coefficients
KW - Weil–Petersson Teichmüller space
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U2 - 10.1007/s12220-022-00946-8
DO - 10.1007/s12220-022-00946-8
M3 - Article
AN - SCOPUS:85130855724
SN - 1050-6926
VL - 32
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 8
M1 - 213
ER -