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Abstract
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We interpolate a new family of Teichmüller spaces
between the universal
Teichmüller space
and its little subspace
.
Each
is defined by
prescribing a subset
of the unit circle as the exceptional set of the vanishing property for
. The inclusion relation
of
induces a natural
inclusion of
, and an
approximation of
by an
increasing sequence of
is investigated. In this paper, we discuss the fundamental properties of
from the
viewpoint of the quasiconformal theory of Teichmüller spaces. We also consider the quotient
space of
by
as
an analog of the asymptotic Teichmüller space.
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Keywords
universal Teichmüller space, symmetric homeomorphism,
asymptotically conformal, Bers embedding, barycentric
extension
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Mathematical Subject Classification 2010
Primary: 30C62, 30F60, 32G15
Secondary: 37E10, 58D05
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Milestones
Received: 26 December 2019
Revised: 16 December 2020
Accepted: 14 August 2021
Published: 10 November 2021
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