arXiv research

New examples show non-integer Hausdorff dimensions in collapsing spaces.

The study extends convergence theorems for Ricci-limit spaces with bounded curvature.

Study the topology of Ricci limit spaces using Gromov-Hausdorff limits.

Ricci limit spaces are semi-locally simply connected.

New examples show strong Kato limits can be branching and not satisfy known conditions.

Study describes limits of surfaces in a mathematical space.

Paper studies convergence of nonnegative scalar curvature metrics to a specific limit space.

Study on the geometry of limit spaces of manifolds with boundary.

Study continuity of limit sets in symmetric spaces.

The paper examines sequences of metric spaces converging to compact limits with specific properties.

The study of random walks on hyperbolic spaces and Teichmüller spaces, proving central limit theorems and geodesic tracking.

Proves limit curve theorem for incomplete metric spaces, applies to null distance in Lorentzian manifolds.

New examples of Ricci limit spaces with mixed tangent cones.

Study on positive scalar curvature and its impact on Ricci limit spaces.

Uniform convergence of metrics on vortex moduli space in Bradlow limit.

If $p : Y \to X$ is an unramified covering map between two compact oriented surfaces of genus at least two, then it is proved that the embedding map, corresponding to $p$, from the Teichmüller space ${\cal T}(X)$, for $X$, to ${\cal T}(Y)$ actually extends to an embedding between the Thurston compactification of the tw…

Kernel methods are studied in a mean field limit for high-dimensional data.

Two groups with specific limit sets in hyperbolic spaces are identified.

Optimal diameter estimates for 3D spaces with non-negative Ricci curvature.

We study the limits of sequences of spheres and complex projective spaces with unbounded dimensions. A sequence of spheres (resp. complex projective spaces) either is a Levy family, infinitely dissipates, or converges to (resp. the Hopf quotient of) a virtual infinite-dimensional Gaussian space, depending on the size o…

Deviation inequalities and limit laws for random walks on metric spaces.

We study direct limits $(G,K) = \varinjlim (G_n,K_n)$ of compact Gelfand pairs. First, we develop a criterion for a direct limit representation to be a multiplicity--free discrete direct sum of irreducible representations. Then we look at direct limits $G/K = \varinjlim G_n/K_n$ of compact riemannian symmetric spaces, …

Introduces new limit spaces for degenerating Calabi-Yau families.

Hausdorff reflection keeps space shape intact.

An inverse limit of a sequence of covering spaces over a given space $X$ is not, in general, a covering space over $X$ but is still a lifting space, i.e. a Hurewicz fibration with unique path lifting property. Of particular interest are inverse limits of finite coverings (resp. finite regular coverings), which yield fi…

We prove that iterated spaces of directions of a limit of a noncollapsing sequence of manifolds with lower curvature bound are topologically spheres. As an application we show that for any finite dimensional Alexandrov space $X^n$ with $n\ge 5$ there exists an Alexandrov space $Y$ homeomorphic to $X$ which can not be o…

We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated variation of twistors and the corresponding limit mixed twistor structures. We construct a compact classifying space for regular singular Briesk…

Penrose limit results for specific 3-surfaces in space-time.

Rare Teichmüller disks converge to small limit sets.

New examples of manifolds in tangent cones of non-collapsed Ricci limit spaces.

Study shows central limit theorem for counting measures in non-smooth spaces.

2-regular points found in spaces with lower Ricci curvature bound.

We show that the Bruschlinsky group with the winding order is a homeomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit …

In this paper, we explore the limit structure of a sequence of Riemannian manifolds with Bakry-Émery Ricci curvature bounded below in the Gromov-Hausdorff topology. By extending the techniques established by Cheeger-Cloding for Riemannian manifolds with Ricci curvature bounded below, we prove that each tangent space at…

We analyze the limit of the p-form Laplacian under a collapse, with bounded sectional curvature and bounded diameter, to a smooth limit space. As an application, we characterize when the p-form Laplacian has small positive eigenvalues in a collapsing sequence.

Paper generalizes Higgs bundle limits to parabolic setting.

In this short note we provide several conjectures on the regularity of measured Gromov-Hausdorff limit spaces of Riemannian manifolds with Ricci curvature bounded below, from the point of view of the synthetic treatment of lower bounds on Ricci curvature for metric measure spaces.

The paper characterizes $G$-ANR spaces and their properties.

Study calculates Kulkarni limit sets for quaternionic projective groups.

The classification of G-spaces by Palais is refined for the case where the orbit space satisfies certain mild topological hypotheses. It is shown that when a sequence of such orbit spaces is "close" to a limit orbit space, in some suitable sense, within a larger ambient orbit space, the G-spaces in the tail of the sequ…

Anosov subgroups' deformations affect limit cones and growth indicators continuously.

The large-N limit of Segal-Bargmann transform on spheres is studied.

We study the behavior under Gromov-Hausdorff convergence of the spectrum of weighted $\barpartial$-Laplacian on compact Kähler manifolds. This situation typically occurs for a sequence of Fano manifolds with anticanonical Kähler class. We apply it to show that, if an almost smooth Fano-Ricci limit space admits a Kähler…

We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a convergent sequence of pyramids. We obtain various applications of our limit formulas as follows. We have a criterion of the phase transition proper…

Paper derives sub-Riemannian versions of Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems for twisted BCV spaces.

Study on metric spaces with properties (ETR), (LBD) and their convergence.

In this paper we study elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular we establish continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrodinger operators, generalized Yamabe constants and…

The paper studies Lagrangian structures in Higgs bundle moduli spaces and their conformal limits.