arXiv research

We introduce a geometric property complementary-finite asymptotic dimension (coas- dim). Similar with asymptotic dimension, we prove the corresponding coarse invariant theorem, union theorem and Hurewicz-type theorem.

Survey on Einstein metrics on domains, linking complex geometry to CR structures.

Research proves unique continuation for Einstein-vacuum equations on aAdS spacetimes.

The study proves properties of intersections of horospheres in harmonic spaces.

Solves constant pre-factor problem for tt*-Toda equations using asymptotic data and symplectic structures.

Asymptotic symmetries of the five dimensional noncompact symmetric space SL(3)/SO(3) are found to form an infinite dimensional Lie algebra, analogously to the asymptotic symmetries of anti-de Sitter spaces in two and three dimensions. Possible exact solvability of the corresponding Chern-Simons theory and the AdS/CFT c…

We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify exact self-similar solutions which correspond to the formal asymptotic expansions …

Research shows persistence diagrams embed into Hilbert space, aiding in their analysis.

Introduce new boundary mass for asymptotically flat half-manifolds

New tractor geometry derived from asymptotically flat spacetimes.

Study the positive mass theorem for certain asymptotic manifolds.

Study reproducing kernels on complex Kepler manifolds.

Detects dense subhypergraphs in heterogeneous random hypergraphs.

We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold. This extends the classical notion of asymptotic directions usually defined on smooth submanifolds. We get a simple expression of these cones for polyhedra in E^3, as well as converge…

Study $b$-$6j$ symbols linking anti-de Sitter tetrahedra to hyperbolic geometry.

We establish Carleman inequalities for the weighted laplacian associated to an expanding gradient Ricci soliton. As a consequence, a unique continuation at infinity is proved for asymptotically Ricci flat Ricci expanders. The obstruction at infinity is a symmetric 2-tensor defined on the link of the corresponding asymp…

Paper connects geometric and analytic aspects of Higgs bundles and pleated surfaces.

I'll describe a general geometric setup allowing for a generalization of Rehren duality to asymptotically anti-de Sitter spacetimes whose classical matter distribution is sufficiently well-behaved as to prevent the occurence of singularities in the sense of null geodesic incompleteness. I'll also comment on the issues …

We study an asymptotic Dirichlet problem for Weyl structures on asymptotically hyperbolic manifolds. By the bulk-boundary correspondence, or more precisely by the Fefferman-Graham theorem on Poincaré metrics, this leads to a natural extension of the notion of Branson's $Q$-curvature to Weyl structures on even-dimension…

We give a construction of Kirby weight systems associated to sl(2) and valued into the finite field Z/pZ. We show that it is possible to apply this sequence of weight systems on the universal invariant of framed link. We also show that the corresponding sequence admits a Fermat limit, which defines an asymptotic ration…

The study connects minimal and maximal surfaces in 3D and 3-L space.

Estimates prove existence of curvature flow in curved spaces.

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular he…

We consider a skew ruled surface $Φ$ in the Euclidean space $E^{3}$ and relative normalizations of it, so that the relative normals at each point lie in the corresponding asymptotic plane of $Φ$. We call such relative normalizations and the resulting relative images of $Φ$ \emph{asymptotic}. We determine all ruled surf…

Study on a Bahri-Brezis problem on hyperbolic manifolds.

We describe the asymptotic behavior of Palais-Smale sequences associated to certain Yamabe-type equations on manifolds with boundary. We prove that each of those sequences converges to a solution of the limit equation plus a finite number of "bubbles" which are obtained by rescaling fundamental solutions of the corresp…

Proves positive mass theorem for hyperbolic manifolds with ends.

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of correspondin…

In this paper we study the asymptotic behaviour of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. This implies a full asymptotic expansion of this function on the set where the curvature of the line bundle is non-degener…

New flexible confidence sequences for robust statistical inference.

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Mouta…

The paper proves a new theorem about paths on nilmanifolds.

Study mass and center of mass in flat 3-manifolds, proving existence of foliations.

The abstract proposes a neural network theory using quantum field theory.

Asymptotics of quantum $6j$ symbols corresponding to a hyperbolic tetrahedra is investigated and the first two leading terms are determined for the case that the tetrahedron has a ideal or ultra-ideal vertex. These terms are given by the volume and the determinant of the Gram matrix of the tetrahedron. A relation to th…

We describe the structure of the asymptotic lines near an inflection point of a Lagrangean surface, proving that in the generic situation it corresponds to two of the three possible cases when the discriminant curve has a cusp singularity. Besides being stable in general, inflection points are proved to exist on a comp…

Discretizes projective minimal surfaces using geometric characterizations.

We study asymptotic behavior of positive smooth solutions of the conformal scalar curvature equation in ${\bf R}^n$. We consider the case when the scalar curvature of the conformal metric is bounded between two positive numbers outside a compact set. It is shown that the solution has slow decay if the radial change is …

The study examines determinantal point processes linked to a specific operator on Riemannian manifolds.

Transforms instantons to monopoles for torus products.

The paper analyzes multivariate Hawkes processes and their induced population processes.

Given a Riemann surface $X = (Σ, J)$ we find an expression for the dominant term for the asymptotics of the holonomy of opers over that Riemann surface corresponding to rays in the Hitchin base of the form $(0,0,\cdots,tω_n)$. Moreover, we find an associated equivariant map from the universal cover $(\tildeΣ,\tilde{J})…

In this paper we define a new convergence called "asymptotically conic convergence" in which a smooth family of Riemannian metrics on a fixed compact manifold degenerate to a metric with isolated conic singularity. Our results are: convergence of the spectrum of the geometric Laplacians and uniform convergence of the c…

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that the Cauchy data space (or Dirichlet-to-Neumann map $\mc{N}$) of the Schrödinger operator $Δ+V$ with $V\in C^2(M_0)$ determines uniquely the potential $V$. We also discuss briefly the corresponding consequences for potential scattering at 0 …

Special geometries found in near horizon spacetimes.

Improved estimates for p-Green functions near poles in Euclidean and Riemannian settings.

We continue the study of the operator of generalized Maxwell equations and completely discover the behavior of the solutions of the time-harmonic equations as the frequency tends to zero. Thereby, we identify degenerate operators in terms of special 'polynomially growing' solutions of a corresponding static problem, wh…

Authors prove an asymptotic expansion for spectral zeta functions on discrete tori.