相关论文: Intersection of positive closed currents of higher…

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external…

Let $\kappa'(G)$ be the edge connectivity of $G$ and $G\times H$ the direct product of $G$ and $H$. Let $H$ be an arbitrary dense graph with minimal degree $\delta(H)>|H|/2$. We prove that for any graph $G$, $\kappa'(G\times…

Let $X$ and $Y$ be compact K\"ahler manifolds of dimension $3$. A bimeromorphic map $f:X\rightarrow Y$ is pseudo-isomorphic if $f:X-I(f)\rightarrow Y-I(f^{-1})$ is an isomorphism. Let $T=T^+-T^-$ be a current on $Y$, where $T^{\pm}$ are…

We show that the complex Monge-Ampere equation on a compact Kaehler manifold (X,\omega) of dimension n admits a Holder continuous omega-psh solution if and only if its right-hand side is a positive measure with Holder continuous…

We study higher spin tensor currents in quantum field theory. Scalar, spinor and vector fields admit unique "improved" currents of arbitrary spin, traceless and conserved. Off-criticality as well as at interacting fixed points conservation…

We study bi-warped product submanifolds of nearly Kaehler manifolds which are the natural extension of warped products. We prove that every bi-warped product submanifold of the form $M=M_T\times_{f_1}\! M_\perp\times_{f_2}\! M_\theta$ in a…

Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…

Little is known about the global structure of the basins of attraction of Newton's method in two or more complex variables. We make the first steps by focusing on the specific Newton mapping to solve for the common roots of $P(x,y) =…

A D5 brane winding around a stack of D3 branes can be used as a model of persistent current in a thin superconducting ring, with the number N of D3s corresponding to the number of transverse channels in the ring. We consider, in the large N…

Let $\mathcal M=\langle M, <, +, \dots\rangle$ be an o-minimal expansion of an ordered group, and $P\subseteq M$ a dense set such that certain tameness conditions hold. We introduce the notion of a `product cone' in $\widetilde{\mathcal…

Let $X$ be a connected compact complex manifold admitting a finite surjective map $A \to X$ from a complex torus $A.$ We prove that up to finite \'etale cover, $X$ is a product of projective spaces and a torus.

Positive definite matrices abound in a dazzling variety of applications. This ubiquity can be in part attributed to their rich geometric structure: positive definite matrices form a self-dual convex cone whose strict interior is a…

We study simple current extensions of tensor products of two vertex operator algebras satisfying certain conditions. We establish the relationship between the fusion rule for the simple current extension and the fusion rule for a tensor…

Let $S$ be a compact oriented finite dimensional manifold and $M$ a finite dimensional Riemannian manifold, let ${\rm Imm}_f(S,M)$ the space of all free immersions $\varphi:S \to M$ and let $B^+_{i,f}(S,M)$ the quotient space ${\rm…

We consider positive-(1,1) De Rham currents in arbitrary almost complex manifolds and prove the uniqueness of the tangent cone at any point where the density does not have a jump with respect to all of its values in a neighbourhood. Without…

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…

This paper theoretically discusses the spin current in spin-triplet superconductor / insulator / spin-triplet superconductor junctions. At low temperatures, a midgap Andreev resonant state anomalously enhances not only the charge current…

In the present paper, we establish a general Kawamata-Viehweg-Koll\'ar-Nadel type vanishing theorem for higher direct images in terms of numerical dimension for closed positive currents on compact K\"ahler manifolds, unifying a number of…

We theoretically explore possible unconventional superconductivity induced by weak repulsive interactions in twisted bilayer TMD (e.g. WSe$_2$) in the presence of an out-of-plane electric field. Using renormalization group (RG) analysis, we…

We show that the non pluripolar product of positive currents is a bimeromorphic invariant. Under some natural assumptions, we show that the (weighted) energy associated to big cohomology classes are also bimeromorphic invariants. We compare…