A characterization of biholomorphic automorphisms of Teichmüller space

Mineyama, Ryosuke; Miyachi, Hideki

doi:10.1017/s0305004112000400

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2023

Publication Types

Select...

Other1

Book1

Article1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 24 publications

(26 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on this, he showed that every isometry of the Teichmüller space T (S g,0 ) with the Teichmüller metric is an element of the extended mapping class group MCG ± (S g,0 ), and that every local isometry is the restriction of a global isometry. Since then the isometry rigidity problem of the Teichmüller metric has been extensively studied (see [Roy71], [EK74a], [EK74b], [EG96], [Lak97], [AP98], [Iva01], [Mar03], [EM03], [FW10], [MM13]). This result was extended by Erale-Kra in [EK74a] to the case of Riemann surfaces with n > 0, and in [EK74b] to the case of isometries between Teichmüller spaces.…”

Section: Introductionmentioning

confidence: 99%

Local Rigidity of Teichmüller space with Thurston metric

Pan

2020

Preprint

View full text Add to dashboard Cite

We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces, which is an analogue of Royden's theorem concerning the Teichmüller metric. Consequently, we obtain the local rigidity theorem of the Thurston metric, as well as a new proof of the global rigidity theorem which was first proved by Walsh.

show abstract