相关论文: Jang's equation and its applications to marginally…

We introduce an operation that measures the self intersections of paths on a surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson…

We investigate the exact nature of the superfluid-to-Mott-insulator crossover for interacting bosons on an optical lattice in a one-dimensional, harmonic trap by high-precision density-matrix renormalization-group calculations. The results…

This is the first of a series of two papers which studies the fractional porous medium equation on a Riemannian manifold with isolated conical singularities. In this article, we show $R$-sectoriality for the fractional powers of possibly…

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. In the present paper we find all marginally trapped surfaces with pointwise 1-type Gauss…

Strongly correlated metals close to the Mott transition display unusual transport regimes, together with large spectral weight transfers in optics and photoemission. We briefly review the theoretical understanding of these effects, based on…

We study the classical dynamics of a charged particle in two dimensions, under the influence of a perpendicular magnetic and an in-plane electric field. We prove the surprising fact that there is a finite region in phase space that…

The physics of doping a Mott insulator is investigated in the presence of a solid-vacuum interface. Using the embedding approach for dynamical mean field theory we show that the change in surface spectral evolution in a doped Mott insulator…

This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same…

Our objective is to develop a stratified Morse theory with tangential conditions. We define a continuous strata-wise smooth Morse function on an abstract stratified space by using control conditions and radiality assumptions on the gradient…

The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…

Yan and Chen proved a weak Cartan-type second main theorem for holomorphic curves meeting hypersurfaces in projective space that included truncated counting functions. Here we give an explicit estimate for the level of truncation.

We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can…

We present several rigidity results for initial data sets motivated by the positive mass theorem. An important step in our proofs here is to establish conditions that ensure that a marginally outer trapped surface is "weakly outermost". A…

We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…

As a classical notion equivalent to viscosity solutions, Monge solutions are well understood for stationary Hamilton-Jacobi equations in Euclidean spaces and have been recently studied in general metric spaces. In this paper, we introduce a…

Entanglement of collections of filaments arises in many contexts, such as in polymer melts, textiles and crystals. Such systems are modeled using periodic boundary conditions (PBC), which create an infinite periodic system whose global…

We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…

We study the evolution of hypersurfaces in spacetime initial data sets by their null mean curvature. A theory of weak solutions is developed using the level-set approach. Starting from an arbitrary mean convex, outer untapped hypersurface…

We discuss recent results obtained by the authors, regarding the analysis of the magneto-geostrophic equation: a model proposed by Moffat and Loper to study the geodynamo and turbulence in the Earth's fluid core. We conclude this review by…

In this note, we extend the rigidity of Cheng-Yau gradient estimate in \cite{HXY} to surfaces with lower Ricci curvature bound. Motivated by these sharp Cheng-Yau gradient estimates, pointwise Cheng-Yau gradient estimates for higher…