arXiv research

The paper proves stability in compact finite dimensional Alexandrov spaces using equivariant Gromov--Hausdorff convergence.

Study Gromov-Hausdorff convergence of metric pairs and tuples.

Stability of Wasserstein spaces under various convergence types.

Study uses equivariant topology to measure distances between G metric spaces.

The equivariant Gromov--Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dimension of the group guarantees that the convergence is by Lie homomorphisms. Additional lower bounds on curvature and volume strengthen this…

Study shows dimension constraints for isometry groups in non-collapsed Riemannian manifolds.

The paper studies spectral convergence of connections on vector and principal bundles.

Study shows intrinsic timed Hausdorff convergence leads to Gromov-Hausdorff and big bang convergence.

Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in the equivariant Gromov--Hausdorff topology, then the limit space is equivariantly …

The paper explores null distance convergence for warped product spacetimes.

The paper proves fibration theorems for manifolds with almost nonnegative Ricci curvature.

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

We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature uniformly bounded from below and diameter uniformly bounded above, Gromov-Hausdorff convergence essentially agrees with intrinsic flat convergence.

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

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

We introduce a natural definition of $L^p$-convergence of maps, $p \ge 1$, in the case where the domain is a convergent sequence of measured metric space with respect to the measured Gromov-Hausdorff topology and the target is a Gromov-Hausdorff convergent sequence. With the $L^p$-convergence, we establish a theory of …

Paper uses Gromov-Hausdorff convergence to re-examine surface classification.

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…

Topology of non-orientable spaces without boundary is studied.

The paper establishes a new link between isometries and scaling nonvanishing property in manifolds with Ricci curvature.

The paper connects geometric and topological concepts to bound distances between metric spaces.

Study limits of Kähler submanifolds and prove no holomorphic isometries.

Defines a Gromov-Hausdorff-like distance for Riemannian manifolds.

The paper connects different convergence concepts in geometric analysis.

Paper introduces a new convergence for Lorentzian spaces using causal diamonds.

Study continuity equation on Hopf and Inoue surfaces, proving estimates and convergence.

Study geometric quantization and measured Gromov-Hausdorff convergence of frame bundle metrics.

Study shows convergence of cscK surfaces in Hilbert scheme.

Global existence and convergence of pluriclosed flow on Oeljeklaus-Toma manifolds.

Defines new metrics for Lorentzian spaces and their convergence.

Study shows tori metrics converging to flat under specific conditions.

The paper studies limits of sub-Riemannian Heisenberg manifolds and proves convergence under certain conditions.

We investigate the case of the Kahler-Ricci flow blowing down disjoint exceptional divisors with normal bundle O(-k) to orbifold points. We prove smooth convergence outside the exceptional divisors and global Gromov-Hausdorff convergence. In addition, we establish the result that the Gromov-Hausdorff limit coincides wi…

Flow analysis leads to metric completion in Kähler geometry.

Existence and convergence of ancient Ricci flow solutions on compact homogeneous spaces.

Ricci flows on a torus converge to a doubled area static metric.

Compactness theorem for timed-metric spaces established.

The study proves compactness and structure of Ricci flow limits.

Study on curvature blow-up and convergence of continuity method on Hirzebruch surface.

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 on topological properties and boundaries of RCD(K,N) spaces.

The paper converts metric bounds to distance function Hölder bounds and proves compactness theorems.

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

Proves Einstein metrics can be created by gluing perturbations.

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

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…

Proves torus sequences can't collapse to intervals under curvature bounds.

Study of irreversible metric-measure spaces, proving convergence and stability results.