arXiv subjects

Yandi Wu

Publications and source records attributed to Yandi Wu.

7 recordsLinked to original sources

arXiv2026

Balanced Spanning Trees for Triangular Strip Lattices

A balanced spanning tree is a spanning tree that contains an edge whose removal partitions the vertices into exactly two connected subtrees of equal size. In this paper, we establish explicit recurrence relations for the number of spanning trees in $2 \times n$ triangular strip lattices- obtained by adding a diagonal edge to each square of a $2 \times n$ grid graph- generalizing combinatorial counting techniques introduced by Raff [Raf08]. We then adapt arguments of Gallagher and Tapp [GT25] to count balanced spanning trees of arbitrary triangular strip lattices. We establish sharp asymptotic bounds for the proportion of balanced spanning trees as $n \rightarrow \infty$. Finally, we determine the probability that a spanning tree of a $2 \times n$ triangular strip lattice chosen uniformly at random is balanced as $n \rightarrow \infty$.

math.CO↗

arXiv2026

Counting and entropy for hyperbolic surface amalgams

This paper is about closed hyperbolic surface amalgams with a focus on the growth of the number of closed geodesics. As in the case of surfaces, we show that topological and volume entropies coincide, but we show stark differences in how they behave according to geometric data with upper and lower bounds on the number of closed geodesics which depend on the length of the systole and the length of the pasting curves. In particular, we show that the entropy can increase exponentially in terms of the pasting length in the absence of a lower bound on the systole.

math.GT↗

arXiv2025

Filling Links and Essential Systole

We answer a question of Freedman and Krushkal, producing filling links in any closed, orientable 3-manifold. The links we construct are hyperbolic, and have large essential systole, contrasting earlier geometric constraints on hyperbolic links in 3-manifolds due to Adams-Reid and Lakeland-Leininger.

math.GT↗

arXiv2024

Iso-length-spectral Hyperbolic Surface Amalgams

Two negatively curved metric spaces are iso-length-spectral if they have the same multisets of lengths of closed geodesics. A well-known paper by Sunada provides a systematic way of constructing iso-length-spectral surfaces that are not isometric. In this paper, we construct examples of iso-length-spectral surface amalgams that are not isometric, generalizing Buser's combinatorial construction of Sunada's surfaces. We find both homeomorphic and non-homeomorphic pairs. Finally, we construct a noncommensurable pair with the same weak length spectrum, the length set without multiplicity.

math.GT↗

arXiv2024

Sub-actions for geodesic flows on locally CAT(-1) spaces

We extend a result of Lopes and Thieullen on sub-actions for smooth Anosov flows to the setting of geodesic flow on locally CAT(-1) spaces. This allows us to use arguments originally due to Croke and Dairbekov to prove a volume rigidity theorem for some interesting locally CAT(-1) spaces, including quotients of Fuchsian buildings and surface amalgams.

math.DS↗

arXiv2023

Marked Length Spectrum Rigidity for Surface Amalgams

In this paper, we show that simple, thick negatively curved two-dimensional P-manifolds, a large class of surface amalgams, are marked length spectrum rigid. That is, if two piecewise negatively curved Riemannian metrics (satisfying certain smoothness conditions) on a simple, thick two-dimensional P-manifold assign the same lengths to all closed geodesics, then they differ by an isometry up to isotopy. Our main theorem is a natural generalization of Croke and Otal's celebrated results about marked length spectrum rigidity of negatively curved surfaces.

math.GT↗

arXiv2023

A topologically rigid set of quotients of the Davis complex

A class of topological spaces is topologically rigid if any two spaces with the same fundamental group are also homeomorphic. Topological rigidity, in addition to its intrinsic interest, has been useful for solving abstract commensurability questions. In this paper, we explore the topological rigidity of quotients of the Davis complex of certain right angled Coxeter groups by providing conditions on the defining graphs that obstruct topological rigidity. Furthermore, we explore why topological rigidity is hard to achieve for quotients of the Davis complex. Nonetheless, we conclude by introducing infinitely many infinite topologically rigid subclasses.

math.GT↗