相关论文: Regularity Theorems and Energy Identities for Dira…

The first result in this study is a non-existence theorem for $\alpha-$harmonic mappings. Additionally, a direct connection between the $\alpha-$ harmonic and harmonic maps is made possible via conformal deformation. Second, the instability…

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of soliton-like solutions of these equations.…

We propose a generalization of the so-called rational map ansatz on the Euclidean space $\mathbb{R}^3$, for any compact simple Lie group $G$ such that $G/{\widehat K}\otimes U(1)$ is an Hermitian symmetric space, for some subgroup…

We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R^m into a pseudo-Riemannian manifold which is two times…

In this paper, we revisit the connection between the Riemann-Roch theorem and the zero energy solutions of the two-dimensional Dirac equation in the presence of a delta-function like magnetic field. Our main result is the resolution of a…

We construct the new one-dimensional Dirac Hamiltonians that are spectrally isomorphic (not isospectral) with the known exactly solvable models. Explicit formulas for their spectra and eigenstates are provided. The operators are utilized…

In this paper, the description of biharmonic map equation in terms of the Maurer-Cartan form for all smooth map of a compact Riemannian manifold into a Riemannian symmetric space $(G/K,h)$ induced from the bi-invariant Riemannian metric $h$…

We establish a duality between harmonic maps from Riemann surfaces to hyperbolic 3-space $\mathbb{H}^3$ and harmonic maps from Riemann surfaces to de Sitter three-space $\operatorname{dS}_3$, best viewed as a generalized Gauss map. On the…

Let $M$ be a closed Riemannian surface and $u_n$ a sequence of maps from $M$ to Riemannian manifold $N$ satisfying $$\sup_n(\|\nabla u_n\|_{L^2(M)}+\|\tau(u_n)\|_{L^p(M)})\leq \Lambda$$ for some $p>1$, where $\tau(u_n)$ is the tension field…

The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface $S$ is a function $E_\rho$ on Teichm\"uller space $\Teich$ which is a qualitative invariant of the holonomy representation…

We consider the Riemann-Cartan geometry as a basis for the Einstein-Sciama-Kibble theory coupled to spinor fields: we focus on $f(R)$ and conformal gravities, regarding the flag-dipole spinor fields, type-(4) spinor fields under the…

In this paper, we study an $\alpha$-flow for the Sack-Uhlenbeck functional on Riemannian surfaces and prove that the limiting map by the $\alpha$-flows is a weak solution to the harmonic map flow. By an application of the $\alpha$-flow, we…

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system with a complex projective Hilbert space as its phase space, thus equipped with a Riemannian metric in addition to a symplectic structure.…

We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…

We study the influence of an additional scalar potential on various geometric and analytic properties of Dirac-harmonic maps. We will create a mathematical wish list of the possible benefits from inducing the potential term and point out…

Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds $M$ and $N$ were introduced in search of a natural notion of harmonicity for maps defined on a general even…

Energy identity for harmonic type maps in supercritical dimensions is an important and difficult problem. For sphere-valued harmonic maps, the first breakthrough was achieved by Lin-Rivi\`ere [Duke Math. J. 2002]. In this paper, by adapting…

In this article we study various analytic aspects of interpolating sesqui-harmonic maps between Riemannian manifolds where we mostly focus on the case of a spherical target. The latter are critical points of an energy functional that…

We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…