High energy degeneration of harmonic maps between surfaces and rays in Teichmüller space (Q1184321)

We investigate the asymptotics of degree one harmonic maps between a fixed domain hyperbolic surface and a family of hyperbolic surfaces which are degenerating in the Teichmüller space \((T_ g)\) of compact surfaces of genus \(g>1\); these asymptotics then provide insight into the nature of degeneration of hyperbolic metrics to boundary points of \(\overline{T_ g^{Th}}\), the Thurston compactification of \(T_ g\). The original description of Thurston's compactification [\textit{W. P. Thurston}, Bull. Am. Math. Soc., New Ser. 19, No. 2, 417-431 (1988; Zbl 0674.57008)] treated the measure theory of the asymptotics, and in a previous paper [the author, J. Differ. Geom. 29, No. 2, 449-479 (1989; Zbl 0655.58009)], we discussed an interpretation of this measure theory in terms of harmonic maps; here we concentrate on more geometrical aspects, exposing some of the finer structure of \(\overline{T_ g^{Th}}\).