arXiv subjects

Lizi Guo

Publications and source records attributed to Lizi Guo.

4 recordsLinked to original sources

arXiv2026

Dimension bounds for finite-volume hyperbolic Coxeter polytopes

We prove that a finite-volume hyperbolic Coxeter polytope has dimension at most $81$, substantially improving Prokhorov's bound of $995$. A refinement of Prokhorov's method gives the intermediate bound $162$, while an extension of Vinberg's planar-angle comparison to the finite-volume setting yields the sharper bound. Both arguments combine improved weighting functions with estimates using cusp geometry to control weight contributions of angles at ideal vertices or edges incident to them.

math.GT↗

arXiv2026

Lehmer's number is not an orientable stretch factor in genus six

Let $λ_L \approx 1.17628$ be Lehmer's number. We prove that no pseudo-Anosov homeomorphism of a closed orientable surface of genus six with orientable invariant foliations has stretch factor $λ_L$. This gives a negative answer to a question of Lanneau and Thiffeault on the minimal stretch factor in even genus. As a consequence, the minimal stretch factor $δ_6^{+}$ of such maps is the largest root of $x^{12}-x^{9}-x^{7}+x^{6}-x^{5}-x^{3}+1$, approximately $1.20189$. The proof combines the Lefschetz method of Lanneau and Thiffeault, the standardly embedded train tracks of Hironaka and Tsang, an elementary analysis of the transition digraph, and an obstruction from periodic conjugacy classes in the fundamental group.

math.GT↗

arXiv2026

On the minimality of the compact right-angled 120-cell

We prove that a compact right-angled polytope in hyperbolic 4-space has at least 120 facets, with equality only for the right-angled 120-cell. This answers a question of Potyagailo and Vinberg. As a consequence, the right-angled 120-cell is the unique compact right-angled 4-polytope of minimal volume and f-vector.

math.GT↗

arXiv2026

Several families of incommensurable noncompact hyperbolic Coxeter polytopes

We classify all 141 finite-volume hyperbolic Coxeter five-dimensional polytopes with eight facets, of which 125 are noncompact. Using maximal-cusp density and a noncompact analog of Bogachev-Douba-Raimbault's argument, we construct infinitely many pairwise incommensurable noncompact Coxeter polytopes in dimensions 4, 5, 6, 7, and 9, with the number of commensurability classes growing at least exponentially in volume.

math.GT↗