相关论文: Zero energy critical points of functionals dependi…

In this article, we investigate critical metrics of the volume functional on complete manifolds without boundary. We prove that any critical metric of the volume functional on a connected, complete manifold with parallel Ricci tensor is…

The Euler-Poisson (EP) system models the dynamics of a variety of physical processes, including charge transport, collisional plasmas, and certain cosmological wave phenomena. In this work, we establish sharp critical threshold conditions…

Yau conjectured that a Fano manifold admits a Kahler-Einstein metric if and only if it is stable in the sense of geometric invariant theory. There has been much progress on this conjecture by Tian, Donaldson and others. The Mabuchi energy…

We investigate the energy per particle, static structure factor, and momentum distribution of the uniform electron gas for different conditions defined by the dimensionless temperature $\Theta = 0.25 - 1.0$ and average interparticle…

We study energy functionals associated with quasi-linear Schr\"odinger operators on infinite graphs, and develop characterisations of (sub-)criticality via Green's functions, harmonic functions of minimal growth and capacities. We proof a…

We present a new class of multivariate binning-free and nonparametric goodness-of-fit tests. The test quantity \emph{energy} is a function of the distances of observed and simulated observations in the variate space. The simulation follows…

$C^*$-algebras, group algebras, and the algebra $\mathcal{A}(X)$ of approximable operators on a Banach space $X$ having the bounded approximation property are known to be zero product determined. We are interested in giving a quantitative…

We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…

Let $f$ be a positive smooth function on a close Riemann surface (M,g). The $f-energy$ of a map $u$ from $M$ to a Riemannian manifold $(N,h)$ is defined as $$E_f(u)=\int_Mf|\nabla u|^2dV_g.$$ In this paper, we will study the blow-up…

The phase diagram of a system with two order parameters, with ${\it n_1}$ and $n_2$ components, respectively, contains two phases, in which these order parameters are non-zero. Experimentally and numerically, these phases are often…

This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type \begin{equation*} \left\{\; \begin{aligned} -\Delta_{\Phi_{1}} u&=F_u(x,u,v)+\lambda R_u(x,u,v)\;\text{ in } \Omega& \\…

Let $\Gamma$ be a compact codimension-two submanifold of $\mathbb{R}^n$, and let $L$ be a nontrivial real line bundle over $X = \mathbb{R}^n \setminus \Gamma$. We study the Allen--Cahn functional, \[E_\varepsilon(u) = \int_X \varepsilon…

The semi-linear, elliptic PDE $AC_{\varepsilon}(u):=-\varepsilon^2\Delta u+W'(u)=0$ is called the Allen-Cahn equation. In this article we will prove the existence of finite energy solution to the Allen-Cahn equation on certain complete,…

We prove that Picard-Lindel\"of iterations for an arbitrary smooth normal Cauchy problem for PDE converge if we assume a suitable Weissinger-like sufficient condition. This condition includes both a large class of non-analytic PDE or…

We propose a theory of metals at the spin-density wave quantum critical point in spatial dimension $d=2$. We provide a first estimate of the full set of critical exponents (dynamical exponent $z=2.13$, correlation length $\nu =1.02$, spin…

Several authors have suggested that the surfaces of vanishing potential generated by the electrostatic fields from a distribution of point charges resemble triply periodic minimal surfaces (TPMS) corresponding to the positions of the point…

The main aim of this paper is to prove the existence of certain proper weakly $r$-harmonic ($ES-r$-harmonic) maps. We construct critical points which belong to a family of rotationally symmetric maps $\varphi_a : B^n \to \mathbb{S}^n$,…

We characterize compact metric spaces whose locally flat Lipschitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weaver. We subsequently use this geometric characterization to…

We present a preliminary study of a new phenomena associated with the Euler-Poisson equations -- the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the…

We summarize results on the asymptotics of the two-particle Green functions of interacting electrons in one dimension. Below a critical value of the chemical potential the Fermi surface vanishes, and the system can no longer be described as…