arXiv research

Study bounds Kähler current diameters on manifolds.

Uniform diameter bound for reflection group disk patterns.

Let M be a hyperbolic 3-manifold with nonempty totally geodesic boundary. We prove that there are upper and lower bounds on the diameter of the skinning map of M that depend only on the volume of the hyperbolic structure with totally geodesic boundary, answering a question of Y. Minsky. This is proven via a filling the…

The paper proves a theorem linking ball volume and Uryson width, with applications to 3-sphere metrics.

Estimates Kähler metrics with noncollapsing volume under complex Monge-Ampère constraints.

The paper studies groups formed by two parabolic maps and their properties.

Study quotients of curve complex actions by mapping class group.

The paper establishes bounds on the lengths of geodesics on manifolds with curvature constraints.

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

The diameter function is a topological Morse function.

Proves existence of maps with controlled small curvatures.

The study bounds the effective diameter of graphs with positive Ollivier curvature.

Study large-scale geometry of infinite type surface mapping class groups.

The paper proves diameter bounds and finiteness for amply regular graphs.

Efficient algorithms find solutions in a rare well-connected cluster at low constraint densities.

The paper introduces new functors for cohomology groups of manifolds.

Study Heegaard Floer homology and word metric on Torelli group.

The class of Riemannian orbifolds of dimension n defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian orbifolds with a lower bound on the sectional curvature is …

Let $f\colon \mathbb{S}^1\rightarrow G$ be a surjective map from the standard unit circle to a graph $G$ such that the pre-image of each point has diameter less than $\varepsilon$. If $\varepsilon$ is small enough, does $f$ split as a free factor in $π_1(G)$?

Mathematical analysis of SNE and t-SNE for dimension reduction.

The Kähler-Ricci flow yields bounded diameter and Ricci curvature for minimal models.

Study axisymmetric ideal fluids on 3-manifolds, proving Fredholm properties.

Study $L^2$-cohomology in unbounded geometry manifolds.

In this paper, we show that, under arbitrary bounded Willmore energy assumption, embedded Willmore spheres (or more generally, embedded Willmore spheres under area constraint) with small diameter in a given $3$-dimensional Riemannian manifold $(M, h)$ necessarily concentrate at a critical point of the scalar curvature …

We show that the diameter of the skinning map of an acylindrical hyperbolic 3-manifold M is bounded on thick Teichmueller geodesic rays by a constant depending only on the thickness of the ray and the topological type of the boundary of M.

New unknots with geometric constraints exist, proving a long-standing conjecture.

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

Short proof shows infinite diameter for surface diffeomorphisms.

We show that if the totally geodesic boundary of a compact hyperbolic 3-manifold M has a large collar of depth d, then the diameter of the skinning map of M is no more than A exp(-d) for some A depending only on the genus and injectivity radius of the boundary of M.

For certain manifolds, nonnegative Ricci curvature limits dimension and forces almost abelian fundamental group.

Thickenings of a metric space capture local geometric properties of the space. Here we exhibit applications of lower bounding the topology of thickenings of the circle and more generally the sphere. We explain interconnections with the geometry of circle actions on Euclidean space, the structure of zeros of trigonometr…

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

The paper classifies constraint mappings in optimization problems.

We give a new proof of a theorem of D. Calegari that says that the Cayley graph of a surface group with respect to any generating set lying in finitely many mapping class group orbits has infinite diameter. This applies, for instance, to the generating set consisting of all simple closed curves.

In this paper, we show that any knot group maps onto at most finitely many knot groups. This gives an affirmative answer to a conjecture of J. Simon. We also bound the diameter of a closed hyperbolic 3-manifold linearly in terms of the presentation length of its fundamental group, improving a result of White.

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.

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

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

Eigenfunctions of collapsing Einstein manifolds are almost constant along fibers.

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.

The paper extends Schwarz's lemma to RC-positivity and complex manifolds.