On Geodesic Segments in the Infinitesimal Asymptotic Teichmüller Spaces

Abstract EN

Let A Z ( R ) be the infinitesimal asymptotic Teichmüller space of a Riemann surface R of infinite type.

It is known that A Z ( R ) is the quotient Banach space of the infinitesimal Teichmüller space Z ( R ) , where Z ( R ) is the dual space of integrable quadratic differentials.

The purpose of this paper is to study the nonuniqueness of geodesic segment joining two points in A Z ( R ) .

We prove that there exist infinitely many geodesic segments between the basepoint and every nonsubstantial point in the universal infinitesimal asymptotic Teichmüller space A Z ( D ) by constructing a special degenerating sequence.