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57
Dressing orbits of harmonic maps
 Duke Math. J
, 1995
"... At the heart of the modern theory of harmonic maps from a Riemann surface to a Riemannian symmetric space is the observation that, in this setting, the harmonic map equations have a zero curvature representation [19, 24, 28] and so correspond to loops of flat connections. This fact was first exploit ..."
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Cited by 33 (6 self)
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At the heart of the modern theory of harmonic maps from a Riemann surface to a Riemannian symmetric space is the observation that, in this setting, the harmonic map equations have a zero curvature representation [19, 24, 28] and so correspond to loops of flat connections. This fact was first exploited in the mathematical literature by Uhlenbeck in her
Geometries and symmetries of soliton equations and integrable elliptic systems
 IN SURVEYS ON GEOMETRY AND INTEGRABLE SYSTEMS, ADVANCED STUDIES IN PURE MATHEMATICS, MATHEMATICAL SOCIETY OF JAPAN NORTHEASTERN UNIVERSITY AND UC IRVINE EMAIL ADDRESS: TERNG@NEU.EDU MSRI, BERKELEY, CA 94720 EMAIL ADDRESS: EWANG@MRSI.ORG
, 2002
"... We give a review of the systematic construction of hierarchies of soliton flows and integrable elliptic equations associated to a complex semisimple Lie algebra and finite order automorphisms. For example, the nonlinear Schrödinger equation, the nwave equation, and the sigmamodel are soliton flow ..."
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Cited by 26 (4 self)
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We give a review of the systematic construction of hierarchies of soliton flows and integrable elliptic equations associated to a complex semisimple Lie algebra and finite order automorphisms. For example, the nonlinear Schrödinger equation, the nwave equation, and the sigmamodel are soliton flows; and the equation for harmonic maps from the plane to a compact Lie group, for primitive maps from the plane to a ksymmetric space, and constant mean curvature surfaces and isothermic surfaces in space forms are integrable elliptic systems. We also give a survey of • construction of solutions using loop group factorizations, • PDEs in differential geometry that are soliton equations or elliptic integrable systems, • similarities and differences of soliton equations and integrable elliptic
Harmonic Maps into Symmetric Spaces and Integrable Systems
"... this article we shall suppose that all manifolds, structures on them and maps between them are smooth, i.e. C ..."
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Cited by 18 (0 self)
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this article we shall suppose that all manifolds, structures on them and maps between them are smooth, i.e. C
Integrable Systems, Harmonic Maps and the Classical Theory of Surfaces
 Aspects Math
, 1994
"... this paper. ..."
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Hamiltonian stationary tori in complex projective plane
, 310
"... We analyze here Hamiltonian stationary surfaces in the complex projective plane as (local) solutions to an integrable system, formulated as a zero curvature equation on a loop group. As an application, we show in details why such tori are finite type solutions, and eventually describe the simplest o ..."
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Cited by 11 (1 self)
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We analyze here Hamiltonian stationary surfaces in the complex projective plane as (local) solutions to an integrable system, formulated as a zero curvature equation on a loop group. As an application, we show in details why such tori are finite type solutions, and eventually describe the simplest of them: the homogeneous ones.
ON THE MODULI OF CONSTANT MEAN CURVATURE CYLINDERS OF FINITE TYPE IN THE 3SPHERE
, 2008
"... We show that onesided Alexandrov embedded constant mean curvature cylinders of finite type in the 3sphere are surfaces of revolution. This confirms a conjecture by Pinkall and Sterling that the only embedded constant mean curvature tori in the 3sphere are rotational. ..."
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Cited by 10 (1 self)
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We show that onesided Alexandrov embedded constant mean curvature cylinders of finite type in the 3sphere are surfaces of revolution. This confirms a conjecture by Pinkall and Sterling that the only embedded constant mean curvature tori in the 3sphere are rotational.
Some geometrical aspects of the 2dimensional Toda equations
 In Geometry, topology and physics (Campinas
, 1996
"... ..."
Isometric immersions of space forms and soliton theory
 Math. Ann
, 1996
"... The study of isometric immersions of space forms into space forms is a classical problem of differential geometry. In its simplest form it arises as the study of surfaces in 3space of constant (nonzero) Gaussian curvature. In this case the integrability condition reduces to the sin resp. sinhGord ..."
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Cited by 10 (1 self)
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The study of isometric immersions of space forms into space forms is a classical problem of differential geometry. In its simplest form it arises as the study of surfaces in 3space of constant (nonzero) Gaussian curvature. In this case the integrability condition reduces to the sin resp. sinhGordon equations. Due to the complicated structure of these equations one
Equivariant harmonic cylinders
"... Abstract. We prove that a primitive harmonic map is equivariant if and only if it admits a holomorphic potential of degree one. We investigate when the equivariant harmonic map is periodic, and as an application discuss constant mean curvature cylinders with screw motion symmetries. ..."
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Cited by 7 (3 self)
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Abstract. We prove that a primitive harmonic map is equivariant if and only if it admits a holomorphic potential of degree one. We investigate when the equivariant harmonic map is periodic, and as an application discuss constant mean curvature cylinders with screw motion symmetries.