arXiv research

Study on compact Quasi-Einstein manifolds yields diameter estimates and Hitchin-Thorpe inequality conditions.

The diameter function is a topological Morse function.

We generalize the maximal diameter sphere theorem due to Toponogov by means of the radial curvature. As a corollary to our main theorem, we prove that for a complete connected Riemannian $n$-manifold $M$ having radial sectional curvature at a point bounded from below by the radial curvature function of an ellipsoid of …

The diameter of a disc filling a loop in the universal covering of a Riemannian manifold may be measured extrinsically using the distance function on the ambient space or intrinsically using the induced length metric on the disc. Correspondingly, the diameter of a van Kampen diagram filling a word that represents the i…

Sharp upper diameter limit found for Ricci solitons.

Maximal distortion between geodesic and Euclidean diameters in polygonal domains is studied.

In this paper we study the Weil-Petersson geometry of $\overline{\mathcal{M}_{g,n}}$, the compactified moduli space of Riemann surfaces with genus g and n marked points. The main goal of this paper is to understand the growth of the diameter of $\overline{\mathcal{M}_{g,n}}$ as a function of $g$ and $n$. We show that t…

New proof for curvature and diameter estimates on Fano manifolds.

In this paper, we shall give a new upper diameter estimate for complete Riemannian manifolds in the case that the Bakry-Émery Ricci curvature has a positive lower bound and the norm of the potential function has an upper bound. Our diameter estimate improves previous ones obtained by Wei and Wylie (J. Differential Geom…

Paper bounds Kähler manifolds' diameter using Orlicz spaces and complex Monge-Ampère equations.

Infinite diameter proved for contractible loops space.

Note removes degeneracy in Kähler geometry estimates.

The study finds a diameter bound for graphs with positive entropic Ricci curvature, with optimal bounds for arithmetic mean.

We prove that the cardinality of the torsion subgroups in homology of a closed hyperbolic manifold of any dimension can be bounded by a doubly exponential function of its diameter. It would follow from a conjecture by Bergeron and Venkatesh that the order of growth in our bound is sharp. We also determine how the numbe…

Study shows shortest geodesic length on certain manifolds is limited by volume, diameter, and cover elements.

In the celebrated book entitled Metric Structures for Riemannian and Non-Riemannian Spaces, so-called Green Book, Gromov presented a problem regarding a metric measure space. Gromov posed the question Bound the expansion coefficient from below in terms of the observable diameter. The overall aim of the current study is…

We prove that if a complete connected $n$-dimensional Riemannian manifold $M$ has radial sectional curvature at a base point $p\in M$ bounded from below by the radial curvature function of a two-sphere of revolution $\widetilde M$ belonging to a certain class, then the diameter of $M$ does not exceed that of $\widetild…

The paper estimates the diameter of $(m,ρ)$-quasi Einstein manifolds under specific conditions.

Torus covers have controlled volume and diameter under curvature and diameter bounds.

Short proof shows infinite diameter for surface diffeomorphisms.

The study shows how many diameter directions in Besse manifolds relate to Blaschke manifolds.

Exact diameter found for some Riemann surfaces.

The paper proves that Kähler manifolds with positive holomorphic sectional curvature have a limited diameter.

Sharp diameter bounds for Calabi-Yau degenerations proved.

Sharp bound on smallest diameter of hyperbolic surfaces.

Maximal diameter theorem for graphs with positive Ricci curvature.

Spheres can be stretched to have larger diameter than antipodal distance.

Max diameter Kahler manifolds with positive bisectional curvature are complex projective spaces.

Makeev proved that among centrally symmetric four-dimensional polytopes, with more than twenty facets and circumscribed about the Euclidean ball of diameter one, there is no universal cover for the family of unit diameter sets. In this paper we examine the converse problem, and prove that each centrally symmetric polyt…

Small sub-Riemannian balls have diameter close to twice their radius.

Extends diameter bounds for submanifolds with boundary and minor curvature restrictions.

Uniform estimates for Kaehler metrics' diameters and volumes.

Study on RCD(0,N) spaces with small linear diameter growth.

Estimates Kaehler metrics' diameter in big cohomology classes.

Study bounds Kähler current diameters on manifolds.

Study systoles and diameters on hyperbolic surfaces, finding an upper bound for their ratio.

Upper diameter bound for manifolds with positive scalar curvature.

Weak base-point freeness leads to Kähler-Ricci flow diameter bounds.

Paper bounds surface diameter and solves Plateau-Douglas problem.

Uniform diameter bounds for Calabi-Yau fibrations with singular fibers.

This paper proves a new, more precise version of Cheng's maximal diameter theorem for manifolds with positive Ricci curvature.

Estimates graph curvature and diameter using Laplacian eigenvalues.

For an immortal Ricci flow on an $m$-dimensional $(m\ge 3)$ closed manifold, we show the following convergence results: (1) if the curvature and diameter are uniformly bounded, then any unbounded sequence of time slices sub-converges to a Riemannian orbifold; (2) if the flow is type-III with diameter growth controlled …

In this paper we show that, under some curvature assumptions the integral of distance function on a compact Riemannian manifold is bounded below by the product of diameter, volume and a constant only depending on the dimension.

Estimates submanifold diameters in curved spaces.

Estimates Kähler metric diameters with entropy bound alone.

Study diameter bounds on Kähler and quaternionic Kähler manifolds with positive curvature.

Uniform diameter bound for reflection group disk patterns.