Related papers: On energy-critical half-wave maps into $\mathbb{S}…

In this paper, we show the nondegeneracy of positive bubble solutions for generalized energy-critical Hartree equations (NLH) \begin{equation*} -{\Delta u}\sts{x} -{\bm\alpha}\sts{N,\lambda} \int_{\R^N} { \frac{…

We extend Siu's and Sampson's celebrated rigidity results to non-compact domains. More precisely, let $M$ be a smooth quasi-projective variety with universal cover $\tilde M$ and let $\tilde X$ be a symmetric space of non-compact type, a…

The purpose of this paper is to present our study on the restoration of the Lorentz symmetry for a Lifshitz-type scalar theory in the infrared region by using nonperturbative methods. We apply the Wegner-Houghton equation, which is one of…

For the class of approximate harmonic maps $u\in W^{1,2}(\Sigma,N)$ from a closed Riemmanian surface $(\Sigma,g)$ to a compact Riemannian manifold $(N, h)$, we show that (i) the so-called energy identity holds for weakly convergent…

Let M = R n or possibly a Riemannian, non compact manifold. We consider semi-excited resonances for a h-differential operator H(x, hD x ; h) on L 2 (M) induced by a non-degenerate periodic orbit $\gamma$ 0 of semi-hyperbolic type, which is…

We introduce and study an approximate solution of the p-Laplace equation, and a linearlization $L_{\epsilon}$ of a perturbed p-Laplace operator. By deriving an $L_{\epsilon}$-type Bochner's formula and a Kato type inequality, we prove a…

We consider the focusing inhomogeneous nonlinear Schr\"odinger equation \[ i\partial_t u + \Delta u + |x|^{-b}|u|^\alpha u = 0\qtq{on}\R\times\R^N, \] with $\alpha=\tfrac{4-2b}{N-2}$, $N=\{3,4,5\}$ and $0<b\leq…

In this paper, we first study the $\alpha-$energy functional, Euler-Lagrange operator and $\alpha$-stress energy tensor. Second, it is shown that the critical points of $\alpha-$ energy functional are explicitly related to harmonic maps…

We study the affine variety $L_{n}(\mathfrak{g})$ of Lie algebra representations, the collection of all homomorphisms from an arbitrary $n$-dimensional Lie algebra into a fixed real semi-simple Lie algebra $\mathfrak{g}$. Using techniques…

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on…

Finite, lossy waveguides are ubiquitous: distributed attenuation with partial reflections produces feedback, resonance, delays and decay across electromagnetic, acoustic, photonic, quantum-transport and electrochemical interfaces. Yet…

We explore the states of matter arising from the spontaneous symmetry breaking (SSB) of $\mathbb{Z}_2$ non-onsite symmetries. In one spatial dimension, we construct a frustration-free lattice model exhibiting SSB of a non-onsite symmetry,…

We study the blow-up dynamics for the energy-critical 1-corotational wave maps problem with 2-sphere target. In arXiv:0911.0692, Rapha\"el and Rodnianski exhibited a stable finite time blow-up dynamics arising from smooth initial data. In…

We determine the symmetry of Cooper pairs, on the basis of the perturbation theory in terms of the Coulomb interaction $U$, for the two-dimensional Hubbard model on the square lattice. The phase diagram is investigated in detail. The…

In 1981, Sacks and Uhlenbeck introduced their famous $\alpha$-energy as a way to approximate the Dirichlet energy and produce harmonic maps from surfaces into Riemannian manifolds. However, the second and third authors together with…

In this paper we consider sequences $u_j:B_2\subseteq M\to N$ of stationary harmonic maps between smooth Riemannian manifolds with uniformly bounded energy $E[u_j]\equiv \int |\nabla u_j|^2\leq \Lambda$ . After passing to a subsequence it…

We show that the energy critical Wave Maps equation from $\mathbb{R}^{2+1}$ to $\mathbb{S}^2$ and restricted to the co-rotational setting with co-rotation index $k = 2$ admits finite time blow up solutions of finite energy on $(0,…

We discuss modifications to the Hawking spectrum that arise when the asymptotic states are supertranslated or superrotated. For supertranslations we find nontrivial off-diagonal phases in the two-point correlator although the emission…

The energy level statistics of the Hubbard model for $L \times L$ square lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for a wide range of the coupling strength. All known symmetries of the model (space, spin…

We consider nonlocal linear Schr\"odinger-type critical systems of the type \begin{equation}\label{eqabstr} \Delta^{1/4} v=\Omega\, v~~~\mbox{in $\R\,.$} \ \end{equation} where $\Omega$ is antisymmetric potential in $L^2(\R,so(m))$, $v$ is…