arXiv research

Study describes limits of surfaces in a mathematical space.

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

Newly discovered Eguchi-Hanson metric arises from edge metrics.

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

Study G-H limits of surfaces with boundary, focusing on same Euler characteristic.

This paper constructs a function on Gromov-Hausdorff limits of 2-surfaces with curvature constraints.

Study shows local topologies of certain geometric spaces.

Study shows properties of Gromov-Hausdorff limit of frame bundles for non-collapsed manifolds.

We show that the Gromov-Hausdorff limit of a sequence of leaves in a compact foliation is a covering space of the limiting leaf which is no larger than this leaf's holonomy cover. We also show that convergence to such a limit is smooth instead of merely Gromov-Hausdorff. Corollaries include Reeb's local stability theor…

Triangle comparison for Kaehler manifolds with curvature bounds.

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…

Study shows how 4D geometry becomes semiflat near curvature limits.

Given a sequence of complete(compact or noncompact) Kähler manifolds $M^n_i$ with bisectional curvature lower bound and noncollapsed volume, we prove that the pointed Gromov-Hausdorff limit is homeomorphic to a normal complex analytic space. The complex analytic structure is the natural "limit" of complex structure of …

Novel Ricci flow normalization for homogeneous spaces, focusing on flag manifolds.

Defines new metrics for Lorentzian spaces and their convergence.

This manuscript studies manifolds-with-boundary collapsing in the Gromov-Hausdorff topology. The main aim is an understanding of the relationship of the topology and geometry of a limiting sequence of manifolds-with-boundary to that of a limit space, which is presumed to be without geodesic terminals. The main result e…

We give the definition of $L^p$-convergence of tensor fields with respect to the Gromov-Hausdorff topology and several fundamental properties of the convergence. We apply this to establish a Bochner-type inequality which keeps the term of Hessian on the Gromov-Hausdorff limit space of a sequence of Riemannian manifolds…

Defines orientation for metric measure spaces with Ricci curvature bounds.

Study limits of Kähler submanifolds and prove no holomorphic isometries.

Researchers create metrics on spheres with Ricci curvature ≥1, limiting to Grushin hemisphere.

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

Study limits of curved spaces with boundaries.

The study proves compactness and structure of Ricci flow limits.

The paper characterizes limits of manifolds using Gromov-Hausdorff metric.

Study shows limits of Kähler manifolds with Ricci curvature have specific properties.

We consider sequences of open Riemannian manifolds with boundary that have no regularity conditions on the boundary. To define a reasonable notion of a limit of such a sequence, we examine "$δ$ inner regions" which avoid the boundary by a distance $δ$. We prove Gromov-Hausdorff compactness theorems for sequences of the…

Magnitude is not continuous but may be stable for most finite metric spaces.

Compactifies metrics on K3 surfaces with algebraic description.

This paper studies limits of aspherical manifolds with specific curvature conditions.

Study shows no new Euclidean factors can appear in the limit of CAT(0) spaces.

The paper proves a conjecture about manifold limits and characterizes their structure.

We discuss the behavior of $(λ_{1. p}(M))^{1/p}$ with respect to the Gromov-Hausdorff topology and the variable $p$, where $λ_{1, p}(M)$ is the first positive eigenvalue of the $p$-Laplacian on a compact Riemannian manifold $M$. Applications include new estimates for the first eigenvalues of the $p$-Laplacian on Rieman…

Study limits of Kähler manifolds with bounded Ricci curvature.

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

Uniform estimates lead to Gromov-Hausdorff limits for Hermitian minimal models.

The paper constructs metrics on tori with Ricci bounds and shows Gromov-Hausdorff limits are not always manifolds.

Compactifies moduli of abelian varieties and curves by attaching flat tori.

In this paper we continue to study Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry. Our main focus is on the algebro-geometric meaning of Riemannian tangent cones and rescaled limits.

Study Gromov-Hausdorff limits of K3 surface metrics via moduli compactification.

The paper explores null distance convergence for warped product spacetimes.

Proves Einstein metrics close to orbifolds are gluing of model spaces.

Study collapsing Calabi-Yau metrics and flows on fiber spaces.

The study proposes conjectures on limit spaces of Riemannian manifolds with Ricci curvature.

Study of Calabi-Yau metrics on converging manifolds, resolving conjectures.

We prove that if $Y$ is the Gromov-Hausdorff limit of a sequence of complete manifolds, $M^n_i$, with a uniform lower bound on Ricci curvature then $Y$ has a universal cover.

New theorem on flat tori stability using harmonic maps and Ricci flow.

Study balancing embedding of degenerating Abelian varieties.

The paper examines conditions for Gromov-Hausdorff convergence of metric quotients and provides examples of conic-flat surfaces.