Ontology type: schema:ScholarlyArticle
2019-04
AUTHORSDaniele Rosmondi
ABSTRACTThe Teichmüller space TS(b) of hyperbolic metrics on a surface S with fixed lengths at the boundary components is symplectic. We prove that any sum of infinitesimal earthquakes on S that is tangent to TS(b) is Hamiltonian, by providing a Hamiltonian L. Such function extends the classical length map associated to a compactly supported measured geodesic lamination and shares with it some peculiar properties, such as properness and strict convexity along earthquakes paths under usual topological conditions. As an application, we prove that any non-Fuchsian affine representation of π1(S) into R2,1⋊SO0(2,1) with cocompact discrete linear part is determined by the singularities of the two invariant regular domains in R2,1 pointed out by Barbot, once the boundary lengths are fixed. More... »
PAGES103-136
http://scigraph.springernature.com/pub.10.1007/s10711-018-0342-5
DOIhttp://dx.doi.org/10.1007/s10711-018-0342-5
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