On Harmonic Mappings into Weil-Peterssson Completed Teichmüller Spaces
نویسنده
چکیده
Harmonic mappings into Teichmüller spaces appear in the study of manifolds which are fibrations whose fibers are Riemann surfaces. In this article we will study the existence and uniquenesses questions of harmonic mappings into Teichmüller spaces, as well as some local and global behavior of the harmonic images induced by the Weil-Petersson geometry of Teichmüller spaces.
منابع مشابه
Weil-Petersson Completion of Teichmüller Spaces and Mapping Class Group Actions
Given a surface of higher genus, we will look at the Weil-Petersson completion of the Teichmüller space of the surface, and will study the isometric action of the mapping class group on it. The main observation is that the geometric characteristics of the setting bear strong similarities to the ones in semi-simple Lie group actions on noncompact symmetric spaces.
متن کاملWeil-Petersson geometry of Teichmüller–Coxeter complex and its finite rank property
Resolving the incompleteness of Weil-Petersson metric on Teichmüller spaces by taking metric and geodesic completion results in two distinct spaces, where the Hopf-Rinow theorem is no longer relevant due to the singular behavior of the Weil-Petersson metric. We construct a geodesic completion of the Teichmüller space through the formalism of Coxeter complex with the Teichmüller space as its non...
متن کاملWeil-petersson Metric on the Universal Teichmüller Space I: Curvature Properties and Chern Forms
We prove that the universal Teichmüller space T (1) carries a new structure of a complex Hilbert manifold. We show that the connected component of the identity of T (1), the Hilbert submanifold T0(1), is a topological group. We define a Weil-Petersson metric on T (1) by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that T (1) is a Kähler -Einstei...
متن کاملThe Universal Properties of Teichmüller Spaces
We discuss universal properties of general Teichmüller spaces. Our topics include the Teichmüller metric and the Kobayashi metric, extremality and unique extremality of quasiconformal mappings, biholomorphic maps between Teichmüller space, earthquakes and Thurston boundary.
متن کاملHarmonic Analysis on Heisenberg Nilmanifolds
In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Γ\Hn. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L(Γ\H) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and charac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008