Teichmüller Theory in Riemannian Geometry

By A. Tromba. 2004

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Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces (2003, background): “We restate and prove this claim in the (hyperbolic) language of Teichmüller theory [5], [29].”
Lectures on Holomorphic Curves in Symplectic and Contact Geometry (2010, methodology): “Another alternative, using the correspondence between conformal structures and hyperbolic metrics on stable Riemann surfaces, is explained in [Tro92].”
On the Geometry of Weil-Petersson Completion of Teichmüller Spaces (2004, background): “With respect to this metric, the Teichmüller space T has non-positive sectional curvature (see Tromba [17] or Wolpert [19]) and though the metric is incomplete (Wolpert [20]) —not every Weil-Petersson geodesic can be extended indefinitely—”
Deviation of ergodic averages for area-preserving flows on surfaces of higher genus (2004, background): “Calculations of first and second variation formulas for various functionals on the Teichmüller space are widespread in Teichmüller theory (see for instance [64], [72], [60], [61]).”
The metric geometry of the manifold of Riemannian metrics over a closed manifold (2009, methodology): “We first became interested in their study because of their applications to Teichm¨uller theory, developed by Fischer and Tromba [ 21 ].”