Related papers: Integrability and Vesture for Harmonic Maps into S…
Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…
Motivated by proving the loss of ergodicity in expanding systems of piecewise affine coupled maps with arbitrary number of units, all-to-all coupling and inversion symmetry, we provide ad-hoc substitutes - namely inversion-symmetric maps of…
The massive Thirring model in the non-laboratory coordinates is considered by the Riemann-Hilbert approach. Existence of global solutions is shown for the cases of the associated Riemann-Hilbert problem without eigenvalues or resonances.…
Integrable couplings are associated with non-semisimple Lie algebras. In this paper, we propose a new method to generate new integrable systems through making perturbation in matrix spectral problems for integrable couplings, which is…
The group-theoretical method used to derive horizontal symmetry from neutrino mixing is reviewed and expanded. Some misunderstanding in the literature regarding the result is clarified. The method used previously to find vacuum alignments…
New classes of exact multi-soliton solutions of KP-1 and KP-2 versions of Kadomtsev-Petviashvili equation with integrable boundary condition $u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov are…
Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but…
In this note we prove that, for any integer n, there exist a smooth 4-manifold, homotopic to a K3 surface, defined by applying the link surgery method of Fintushel-Stern to a certain 2-component graph link, which admits n inequivalent…
In this paper we study generic M(atrix) theory compactifications that are specified by a set of quotient conditions. A procedure is proposed, which both associates an algebra to each compactification and leads deductively to general…
We continue our study [Ou4] of f-biharmonic maps and f-biharmonic submanifolds by exploring the applications of f-biharmonic maps and the relationships among biharmonicity, f-biharmonicity and conformality of maps between Riemannian…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
This survey reviews results on harmonic maps into spaces of non-positive curvature, with a focus on targets that lack smooth structure. More precisely, we consider targets that are complete metric spaces with non-positive curvature in the…
We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We obtain an extension of Siu's rigidity to Kahler-Weyl geometry and apply the latter to Vaisman's conjecture. Other applications…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
We study the non-invertible symmetries of class $\mathcal{S}$ theories obtained by compactifying the type $\mathfrak{a}_{p-1}$ 6d (2,0) theory on a genus $g$ Riemann surface with no punctures. After setting up the general framework, we…
In this paper, we derive a Riccati-type equation applicable to (sub-)static Einstein spaces and examine its various applications. Specifically, within the framework of conformally compactifiable manifolds, we prove a splitting theorem for…
In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This…
We consider a generalisation of the p+ip pairing Hamiltonian with external interaction terms. These terms allow for the exchange of particles between the system and its environment. As a result the u(1) symmetry associated with conservation…
We prove rigidity results describing contextually-constrained maps defined on Grassmannians and manifolds of ordered independent line tuples in finite-dimensional vector or Hilbert spaces. One statement in the spirit of the Fundamental…
We explain how to apply techniques from integrable systems to construct $2k$-soliton homoclinic wave maps from the periodic Minkowski space $S^1\times R^1$ to a compact Lie group, and more generally to a compact symmetric space. We give a…