Related papers: Separating Pants Decompositions in the Pants Compl…

Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directions. First, we find bounds on the…

It is well-known that a Riemann surface can be decomposed into the so-called pairs-of-pants. Each pair-of-pants is diffeomorphic to a Riemann sphere minus 3 points. We show that a smooth complex projective hypersurface of arbitrary…

We construct a quasiconformally homogeneous hyperbolic Riemann surface-other than the hyperbolic plane-that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact…

Let $S$ be a closed orientable surface with genus $g\geq 2$. For a sequence $\s_i$ in the Teichm\"uller space of $S$, which converges to a projective measured lamination $[\lam]$ in the Thurston boundary, we obtain a relation between $\lam$…

This paper is the fifth and final in a series on embedded minimal surfaces. Following our earlier papers on disks, we prove here two main structure theorems for non-simply connected embedded minimal surfaces of any given fixed genus. The…

We study two decomposition problems in combinatorial geometry. The first part deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold…

We present a construction of sequences of closed hyperbolic surfaces that have long systoles which form pants decompositions of these surfaces. The length of the systoles of these surfaces grows logarithmically as a function of their genus.

This note is devoted to a trick which yields almost trivial proofs that certain complexes associated to topological surfaces are connected or simply connected. Applications include new proofs that the complexes of curves, separating curves,…

It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal…

Every finite graph $G$ can be decomposed in a canonical way that displays its local connectivity-structure [DJKK26]. These decompositions are defined via a suitable more tree-like covering of $G$, whose tangle-tree structure is projected…

In this paper, we show that a smooth 4-manifold diffeomorphic to a complex hypersurface in $\mathbb{CP}^3 $ of degree $d\geq 5$ can be decomposed as the union of $d(d-4)^2$ copies of 4-dimensional pair-of-pants and certain subsets of K3…

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each…

We consider a union of two pants decompositions of the same orientable 2-dimensional surface of any genus g. Each pants decomposition corresponds to some handlebody bounded by this surface, so two pants decompositions correspond to a…

In this work, we study conditions for the existence of length-constrained path-cycle decompositions, that is, partitions of the edge set of a graph into paths and cycles of a given minimum length. Our main contribution is the…

In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…

Recent neural, physics-based modeling of garment deformations allows faster and visually aesthetic results as opposed to the existing methods. Material-specific parameters are used by the formulation to control the garment inextensibility.…

In this paper we introduce a novel notion of separation surfaces for image decomposition. A surface is embedded in the spectral total-variation (TV) three dimensional domain and encodes a spatially-varying separation scale. The method…

Let $S_{g,n}$ be a surface of genus $g $ with $n$ marked points. Let $X$ be a complete hyperbolic metric on $S_{g,n}$ with $n$ cusps. Every isotopy class $[\gamma]$ of a closed curve $\gamma \in \pi_{1}(S_{g,n})$ contains a unique closed…

In this paper1 , we use the coding developed by R. Bowen and C. Series to compute the number of self-intersections of a closed geodesic on a pair of pants. We give lower and upper bounds on the number of self-intersections of a closed…

Let $\Sigma_{g,n}$ denote the compact orientable surface with genus $g\geq 2$ and boundary disjoint union of $n$ circles. By using a particular pants-decomposition of $\Sigma_{g,n},$ we obtain a formula that computes the Reidemeister…