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Junzhi Huang

Publications and source records attributed to Junzhi Huang.

6 recordsLinked to original sources
arXiv2026

Constructing depth one laminations transverse to pseudo-Anosov flows

Given a pseudo-Anosov flow $ϕ$ on a closed atoroidal $3$--manifold $M$ and a closed surface $S$ almost transverse to $ϕ$, we give a homological characterization of when $S$ can be completed to an almost transverse depth one lamination or foliation whose set of compact leaves is $S$. As a consequence, we show that the cone of classes in $H^1(M\backslash \!\! \backslash S)$ that are positive on the closed orbits of $ϕ$, when nonempty, is an entire foliation cone of $M\backslash \!\! \backslash S$.

math.GT↗
arXiv2026

Pseudo-Anosov flows, hyperbolic geometry, and the curve graph

Starting with a pseudo-Anosov flow $φ$ on a closed hyperbolic $3$-manifold $M$ and an embedded surface $S \subset M$ that is (almost) transverse to $φ$, we relate the hyperbolic geometry of $M$ (e.g. volume, circumference, short geodesics) to dynamical invariants of $φ$ encoded by the curve graph of $S$.

math.GT↗
arXiv2025

Systolic lattice extensions of classical Schottky groups

We produce lattice extensions of a dense family of classical Schottky subgroups of the isometry group of $d$-dimensional hyperbolic space. The extensions produced are said to be systolic, since all loxodromic elements with short translation length are conjugate into the Schottky groups. Various corollaries are obtained, in particular showing that for all $d\geq3$, the set of complex translation lengths realized by systoles of closed hyperbolic $d$-manifolds is dense inside the set of all possible complex translation lengths. We also consider complex translation lengths in arithmetic hyperbolic $d$-manifolds, and provide a new way to construct non-arithmetic lattices.

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arXiv2024

Density of systoles of hyperbolic manifolds

We show that for each $n \geq 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +\infty)$. We also show that for any $n\geq 2$ and any Salem number $λ$, there is a closed arithmetic hyperbolic $n$-manifold of systole $\log(λ)$. In particular, the Salem conjecture holds if and only if the systoles of closed arithmetic hyperbolic manifolds in some (any) dimension fail to be dense in $(0, +\infty)$.

math.GT↗
arXiv2024

Depth-one foliations, pseudo-Anosov flows and universal circles

Given a taut depth-one foliation $\mathcal{F}$ in a closed atoroidal 3-manifold $M$ transverse to a pseudo-Anosov flow $ϕ$ without perfect fits, we show that the universal circle coming from leftmost sections $\mathfrak{S}_\mathrm{left}$ associated to $\mathcal{F}$, constructed by Thurston and Calegari-Dunfield, is isomorphic to the ideal boundary of the flow space associated to $ϕ$ with natural structure maps. As a corollary, we use a theorem of Barthelmé-Frankel-Mann to show that there is at most one pseudo-Anosov flow without perfect fits transverse to $\mathcal{F}$ up to orbit equivalence.

math.GT↗