相关论文: Scalar curvature and the existence of geometric st…

The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order…

Let n be an integer such that 25 \leq n \leq 51. We construct a smooth metric g on S^n with the property that the set of constant scalar curvature metrics in the conformal class of g is not compact.

We argue that in the quantum motion of a scalar particle of mass "m" on S^3_R perturbed by the trigonometric Scarf potential (Scarf I) with one internal quantized dimensionless parameter, \ell, the 3D orbital angular momentum, and another,…

This paper surveys and gives a uniform exposition of results contained in papers published by the team of authors. The subject is degenerations of surfaces, especially to unions of planes. More specifically, we deduce some properties of the…

The decays $\eta'\to3\pi^{0}$ and $\pi^{0}\pi^{+}\pi^{-}$ were consider in isobar model approach. Branching ratio and Dalitz-plot shape of the decay $\eta'\to3\pi^{0}$ can be explain by $a0$- and $\sigma$-meson contributions. The $\sigma$…

Motivated by DeVleming's work on moduli of surfaces in $\mathbb{P}^3$ and Chen-Hu-Jiang's work on moduli of threefolds with volume $2$ and geometric genus $4$, we study the deformation of pairs of $\mathbb{P}^3$ and hypersurfaces using the…

Let $M$ be a compact closed manifold of variable negative curvature. Fix an element $\operatorname{id} \neq \gamma$ in the fundamental group $\Gamma$ of $M$, and denote the set of elements in $\Gamma$ that are conjugate to $\gamma$ by…

We study the evolution of the cosmological perturbations after inflation in curvaton models where the non-relativistic curvaton decays into both radiation and a cold dark matter component. We calculate the primordial curvature and…

We first establish local $C^2$ estimates of solutions to the $\sigma_2$-curvature equation with nonlinear Neumann boundary condition. Then, under assumption that the mean curvature of a background metric is nonnegative on totally…

We determine the local equivalence class of the Seiberg-Witten Floer stable homotopy type of a spin rational homology 3-sphere $Y$ embedded into a spin rational homology $S^{1} \times S^{3}$ with a positive scalar curvature metric so that…

We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by…

The effect of a local shear transformation on plastic deformation of a three-dimensional amorphous solid is studied using molecular dynamics simulations. We consider a spherical inclusion, which is gradually transformed into an ellipsoid of…

We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between $(n+1)$ points in infinitesimally small neighborhoods of a point. Since this characterization is purely in…

This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic…

We study several exotic systems, including the X-cube model, on a flat three-torus with a twist in the $xy$-plane. The ground state degeneracy turns out to be a sensitive function of various geometrical parameters. Starting from a lattice,…

Mutation is an operation on 3-manifolds containing an embedded surface of genus 2. It is defined by cutting along the surface and regluing using the `hyperelliptic' involution, and is known to preserve many 3-manifold invariants. I show…

In this note we clarify the structure of the moduli space of constant scalar curvature Kaehler metrics as one approaches the boundary of the Kaehler cone on cscK manifolds blown up at finite set of points, in the spirit of the previous work…

We study harmonic maps from a 3-manifold with boundary to $\mathbb{S}^1$ and prove a special case of dihedral rigidity of three dimensional cubes whose dihedral angles are $\pi / 2$. Furthermore we give some applications to mapping torus…

We consider the blowup of a point of a compact K\"ahler manifold and a metric of the form $\mu^*h + t b$ on it, where $h$ is a K\"ahler metric on the original manifold and $b$ is Hermitian form that looks like the Fubini--Study metric near…

This work is devoted to the study of deformations of hyperbolic cone structures under the assumption that the lengths of the singularity remain uniformly bounded over the deformation. Given a sequence $(M_{i}%, p_{i}) $ of pointed…