arXiv research

Study quotients of curve complex actions by mapping class group.

Metric WPD for pseudo-Anosov maps shows many unbounded quasi-morphisms.

We study random walks on groups of isometries of non-proper delta-hyperbolic spaces under the assumption that at least one element in the group satisfies Bestvina-Fujiwara's WPD condition. We show that in this case typical elements are WPD, and the Poisson boundary coincides with the Gromov boundary. Moreover, we show …

Study shows Poisson boundary matches hyperbolic boundary for certain groups.

The aim of this note is to give the simplest possible proof that Mapping Class Groups of closed hyperbolic surfaces are acylindrically hyperbolic, and more specifically that their curve graphs are hyperbolic and that pseudo-Anosovs act on them as loxodromic WPDs.

The paper studies hyperbolic quotients of projection complexes and their actions.

Study of groups and their quasi-isometrically embedded subgroups.

New group with non-loxodromic Morse element found.

We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $N\ge 3$ the number of…

Links can be transformed into many others using a specific operation.

We define strongly Gauduchon spaces and the class SG which are generalization of strongly Gauduchon manifolds in complex spaces. Comparing with the case of Kahlerian, the strongly Gauduchon space and the class SG are similar to the Kahler space and the Fujiki class C respectively. Some properties about these complex sp…

New spacetimes found that are refocusing but not strongly refocusing.

Study of strongly invertible Legendrian links in contact 3-space.

In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones SG in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence…

We investigate refocusing and strong refocusing of light rays in a space-time. A strongly refocusing space-time is refocusing. The converse is unknown. We construct examples of space-times which are refocusing, but not strongly so, at a particular point. These space-times are strongly refocusing at other points. The ge…

Strongly convex bodies can be approximated by smooth ones.

Study on invariant Seifert surfaces for strongly invertible knots, showing large gaps in genus.

Table of symmetric diagrams for knots up to 10 crossings.

New algorithm proves most inflexible manifolds are not strongly inflexible.

New examples of Howson groups that are not strongly Howson found.

The paper simplifies strongly convex problems to simplicial structures.

Develops equivariant grid homology for strongly invertible knots.

New findings on knot genera using advanced techniques.

The paper proves a Schwarz lemma for weakly Kähler-Finsler manifolds.

A surface automorphism is strongly irreducible if every essential simple closed curve in the surface has nontrivial geometric intersection with its image. We show that a three-manifold admits only finitely many inequivalent surface bundle structures with strongly irreducible monodromy.

Specialized knot theory theorems for strongly involutive links.

Study proves obstructions to equivariantly slice strongly negative amphichiral knots.

The aim of this article is to give a characterization of strongly quasipositive quasi-alternating links and detect new classes of strongly quasipositive Montesinos links and non-strongly quasipositive Montesinos links. In this direction, we show that, if $L$ is an oriented quasi-alternating link with a quasi-alternatin…

Defines knot signature invariant using G-signature theorem.

The study classifies strongly irreducible Heegaard splittings in hyperbolic 3-manifolds.

In this paper we generalize the notion of strongly poly-free group to a larger class of groups, we call them strongly poly-surface groups and prove that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for any virtually strongly poly-surface g…

Smooth families of biholomorphisms between strongly pseudoconvex domains are shown to be smooth.

The paper defines new types of positivity and proves properties of Schur forms for vector bundles.

We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kaehler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.

Strongly polynomial algorithm for approximate Forster transforms and halfspace learning.

In this paper, we prove that a strongly convex complex Finsler metric $F$ on a domain $D\subset\mathbb{C}^n$ is projectively flat (resp. dually flat) if and only if $F$ comes from a strongly convex complex Minkowski metric.

In Garside groups, axes of Morse elements are strongly contracting.

Study identifies prime strongly positive amphicheiral knots with double symmetry.

The paper defines new geometric concepts on Riemannian manifolds and applies them to optimization problems.

Two knots with unique surgery properties.

The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.

Two new algorithms solve nonconvex-strongly concave problems efficiently.

In this paper we define strongly projectively flatness of holomorphic maps into the complex Grassmannian manifold, which is a kind of generalization of holomorphic maps into the complex projective space and prove a rigidity of equivariant strongly projectively flat maps of compact simply connected homogeneous Kähler ma…

Study non-fibered links' relation to tight contact structures.

This paper classifies strongly nilpotent special multi-flags and their Goursat counterparts.

The paper proves properties of complex Finsler metrics on specific domains.

New spectral sequences define knot invariants.

Geodesic orbit metrics proven on specific homogeneous spaces.