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5 papers · 2 filters
Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms
Boris Khesin, Jonatan Lenells, Gerard Misiolek
We study an equation lying `mid-way' between the periodic Hunter-Saxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magne…
Poisson geometry and first integrals of geostrophic equations
Boris Khesin, Paul Lee
We describe first integrals of geostrophic equations, which are similar to the enstrophy invariants of the Euler equation for an ideal incompressible fluid. We explain the geometry…
Goldman flows on the Jacobian
Lisa C. Jeffrey, David B. Klein
We show that the Goldman flows preserve the holomorphic structure on the moduli space of homomorphisms of the fundamental group of a Riemann surface into U(1), in other words the J…
Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds
Spyridon Alexakis, Rafe Mazzeo
If is a properly embedded minimal surface in a convex cocompact hyperbolic 3-manifold with boundary at infinity an embedded curve , then Graham and Witten showed how to…
Families index for manifolds with hyperbolic cusp singularities
Pierre Albin, Frederic Rochon
Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant's treatment of Dirac-type oper…