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An upper bound of the total Q-curvature and its isoperimetric deficit for higher-dimensional conformal Euclidean metrics

On the concentration-compactness phenomenon for the first Schrodinger eigenvalue

Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori

Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations

Radial and non radial solutions for Hardy–Hénon type elliptic systems

Domain branching in uniaxial ferromagnets: asymptotic behavior of the energy

Weak convergence of currents and cancellation

A smooth global branch of solutions for a semilinear elliptic equation on $${\mathbb{R}^N}$$

Jacobians of Sobolev homeomorphisms

Gamma-convergence and the emergence of vortices for Ginzburg–Landau on thin shells and manifolds

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Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori

Content Provider	Springer Nature Link
Author	Romon, Pascal Leschke, Katrin
Copyright Year	2009
Abstract	The multiplier spectral curve of a conformal torus f : T 2 → S 4 in the 4-sphere is essentially (Bohle et al., Conformal maps from a 2-torus to the 4-sphere. arXiv:0712.2311) given by all Darboux transforms of f. In the particular case when the conformal immersion is a Hamiltonian stationary torus $${f: T^2 \to\mathbb{R}^4}$$ in Euclidean 4-space, the left normal N : M → S 2 of f is harmonic, hence we can associate a second Riemann surface: the eigenline spectral curve of N, as defined in Hitchin (J Differ Geom 31(3):627–710, 1990). We show that the multiplier spectral curve of a Hamiltonian stationary torus and the eigenline spectral curve of its left normal are biholomorphic Riemann surfaces of genus zero. Moreover, we prove that all Darboux transforms, which arise from generic points on the spectral curve, are Hamiltonian stationary whereas we also provide examples of Darboux transforms which are not even Lagrangian.
Ending Page	74
Page Count	30
Starting Page	45
File Format	PDF
ISSN	09442669
e-ISSN	14320835
Journal	Calculus of Variations and Partial Differential Equations
Issue Number	1-2
Volume Number	38
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-10-17
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lagrangian submanifolds; Maslov index Immersions (minimal, prescribed curvature, tight, etc.) Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Theoretical, Mathematical and Computational Physics Analysis Surfaces in Euclidean space
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori

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