arXiv research

We describe and construct here pseudo-Hermitian structures $θ$ without torsion (i.e. with transversal symmetry) whose Webster-Ricci curvature tensor is a constant multiple of the exterior differential $dθ$. We call these structures pseudo-Hermitian Einstein and our result states that they all can be derived locally fro…

We obtain a necessary and sufficient condition of existence of a K{ä}hler-Einstein metric on a $G\times G$-equivariant Fano compactification of a complex connected reductive group $G$ in terms of the associated polytope. This condition is not equivalent to the vanishing of the Futaki invariant. The proof relies on the …

The paper studies Ricci curvature on Kähler-Ricci flow.

Continuity of complex Monge-Ampère potentials on Kähler manifolds.

The paper proves conditions for Kähler manifolds with negative curvature.

In 2D, a conjecture about the Ricci tensor of Kähler-Einstein metrics for convex bodies is verified.

The study establishes conditions for stratified spaces to satisfy RCD(K, N) curvature-dimension condition.

Study shows convergence of Fubini-Study currents to equilibrium metrics on Kähler manifolds.

We show how the fundamental cocycles on current Lie algebras and the Lie algebra of symmetries for the sigma model are obtained via the current algebra functors. We present current group extensions integrating some of these current Lie algebra extensions.

Study the intersection of positive closed currents using tangent currents and King's residue formula.

Proves unique continuation for area minimizing currents.

The paper extends geometric surface properties to currents tangent to smooth distributions.

Constructs brane current algebras from QP-manifolds, generalizing string currents.

Current-mode memristor crossbars enable neuromemristive systems with similar accuracy but different weight distributions.

New findings on currents and Frobenius theorem properties.

New metric on geodesic currents connects different surface genera.

New approach uses $k$-currents for data modeling, leading to interpretable latent representations.

Introduces Lie group actions in smoothing processes for currents and spaces with curvature.

Defines currents relative to a free factor system and proves dynamics for fully irreducible automorphisms.

To a tropical $p$-cycle $V_{\mathbb{T}}$ in $\mathbb{R}^n$, we naturally associate a normal closed and $(p,p)$-dimensional current on $(\mathbb{C}^*)^n$ denoted by $\mathscr{T}_n^p(V_{\mathbb{T}})$. Such a "tropical current" $\mathscr{T}_n^p(V_{\mathbb{T}})$ will not be an integration current along any analytic set, si…

Defines a new distance for integral current spaces and proves convergence criteria.

Currents on cusped hyperbolic surfaces have a denseness property similar to compact surfaces.

New characterization of geodesic currents via curve functionals.

The paper connects bundle curvature to random zero currents.

We construct new examples of normal (metric) currents using inverse systems of cube complexes. For any $N\ge 2$ we provide examples of $N$-dimensional normal currents whose associated vector fields are simple, and whose supports are purely $2$-unrectifiable and have Nagata dimension $N$. We show that in $l^\infty$ norm…

Recently, a new embedding/compactness theorem for integral currents in a sequence of metric spaces has been established by the second author. We present a version of this result for locally integral currents in a sequence of pointed metric spaces. To this end we introduce another variant of the Ambrosio--Kirchheim theo…

This paper defines and studies currents and slices in the Heisenberg group, with new challenges and insights.

New insights into currents of Hitchin representations with combinatorial restrictions.

We define generalized currents associated with immersions of abstract solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geometric De…

Explains length functions on currents and their applications to dynamics and counting.

Study critical exponent for geodesic currents using quasi-metric spaces.

New definition of metric current yields Finsler geometry volume densities.

Introduces Lebesgue currents for real intersection theory.

We consider the problem of identifying current coupons for Agency backed To-be-Announced (TBA) Mortgage Backed Securities. In a doubly stochastic factor based model which allows for prepayment intensities to depend upon current and origination mortgage rates, as well as underlying investment factors, we identify the cu…

Constructs currents and heights on K3 surfaces.

Study real rectifiable currents, generalize King's theorem, simplify proof, relate to Hodge conjecture.

We relate Ambrosio-Kirchheim metric currents to Alberti representations and Weaver derivations. In particular, given a metric current $T$, we show that if the module $\mathscr{X}(\|T\|)$ of Weaver derivations is finitely generated, then $T$ can be represented in terms of derivations; this extends previous results of Wi…

We discuss positive closed currents and Fubini-Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini-Study currents associated to high powers of a semipositive singular line bundle converge weakly to the curvature current on the set where the curva…

Generalized current algebras introduced by Alekseev and Strobl in two dimensions are reconstructed by a graded manifold and a graded Poisson brackets. We generalize their current algebras to higher dimensions. QP manifolds provide the unified structures of current algebras in any dimension. Current algebras give rise t…

New currents derived from Killing-Yano tensors for gravity.

We generalize subset currents on hyperbolic groups to surfaces.

The paper shows how Sobolev maps affect currents in metric spaces.

Extends classification of invariant measures on geodesic currents.

Currents on Lie groups form a Hopf algebra structure.

We show that symmetries and gauge symmetries of a large class of 2-dimensional sigma models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the sigma model. We compute the current-current commutator and analyse the anomaly cancell…

Geodesic currents on hyperbolic surfaces have dual spaces that are metric trees.

Computes mapping classes for currents on compact surfaces.

The paper proves existence and partial regularity for Legendrian area-minimizing currents.