The VMO-Teichmüller space and the variant of Beurling–Ahlfors extension by heat kernel

Huaying Wei; Katsuhiko Matsuzaki

doi:10.1007/s00209-022-03104-6

The VMO-Teichmüller space and the variant of Beurling–Ahlfors extension by heat kernel

Huaying Wei, Katsuhiko Matsuzaki^*

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.

Original language	English
Pages (from-to)	1739-1760
Number of pages	22
Journal	Mathematische Zeitschrift
Volume	302
Issue number	3
DOIs	https://doi.org/10.1007/s00209-022-03104-6
Publication status	Published - 2022 Nov

Keywords

A-weight
BMO function
Beurling–Ahlfors extension
VMO Teichmüller space
Vanishing Carleson measure

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00209-022-03104-6

Cite this

@article{6767c75f3f8b4b1d82bdad4d0a6f5793,

title = "The VMO-Teichm{\"u}ller space and the variant of Beurling–Ahlfors extension by heat kernel",

abstract = "We give a real-analytic section for the Teichm{\"u}ller projection onto the VMO-Teichm{\"u}ller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichm{\"u}ller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichm{\"u}ller space admits a real-analytic contraction mapping.",

keywords = "A-weight, BMO function, Beurling–Ahlfors extension, VMO Teichm{\"u}ller space, Vanishing Carleson measure",

author = "Huaying Wei and Katsuhiko Matsuzaki",

note = "Funding Information: Research supported by Japan Society for the Promotion of Science (KAKENHI 18H01125 and 21F20027) Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = nov,

doi = "10.1007/s00209-022-03104-6",

language = "English",

volume = "302",

pages = "1739--1760",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - The VMO-Teichmüller space and the variant of Beurling–Ahlfors extension by heat kernel

AU - Wei, Huaying

AU - Matsuzaki, Katsuhiko

PY - 2022/11

Y1 - 2022/11

N2 - We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.

AB - We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.

KW - A-weight

KW - BMO function

KW - Beurling–Ahlfors extension

KW - VMO Teichmüller space

KW - Vanishing Carleson measure

UR - http://www.scopus.com/inward/record.url?scp=85137490245&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85137490245&partnerID=8YFLogxK

U2 - 10.1007/s00209-022-03104-6

DO - 10.1007/s00209-022-03104-6

M3 - Article

AN - SCOPUS:85137490245

SN - 0025-5874

VL - 302

SP - 1739

EP - 1760

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

ER -

The VMO-Teichmüller space and the variant of Beurling–Ahlfors extension by heat kernel

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this