Hamiltonian properties of earthquake flows on surfaces with closed geodesic boundary View Full Text


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Article Info

DATE

2019-04

AUTHORS

Daniele Rosmondi

ABSTRACT

The 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... »

PAGES

103-136

References to SciGraph publications

Journal

TITLE

Geometriae Dedicata

ISSUE

1

VOLUME

199

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10711-018-0342-5

DOI

http://dx.doi.org/10.1007/s10711-018-0342-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101547095


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