Related papers: Filling a Hole in a Crease Pattern: Isometric Mapp…

We consider pointed Lorentzian manifolds and construct "canonical" foliations by constant mean curvature (CMC) hypersurfaces. Our result assumes a uniform bound on the local sup-norm of the curvature of the manifold and on its local…

We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.

We develop a framework for characterizing isometric immersions of simply connected, bounded, planar regions with piecewise smooth boundaries into three-dimensional space. Each immersion is associated with a framed curve along the boundary…

Programming the non-uniform growth of a responsive polymer gel has emerged as a powerful tool to shape sheets into prescribed three dimensional shapes. We demonstrate that shapes with zero Gaussian curvature, except at singularities,…

Embedding models trained separately on similar data often produce representations that encode stable information but are not directly interchangeable. This lack of interoperability raises challenges in several practical applications, such…

We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the Kapovich-Millson moduli space of polygons isomorphic to the boundary. For a generic polyhedral disk we…

Geometric stress focusing, e.g. in a crumpled sheet, creates point-like vertices that terminate in a characteristic local crescent shape. The observed scaling of the size of this crescent is an open question in the stress focusing of…

A simplicial complex $X$ is said to be tight with respect to a field $\mathbb{F}$ if $X$ is connected and, for every induced subcomplex $Y$ of $X$, the linear map $H_\ast (Y; \mathbb{F}) \rightarrow H_\ast (X; \mathbb{F})$ (induced by the…

In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out…

In the first part of this paper, we extend the result of Li-Wang on the linearized embedding problem to a compact manifold of arbitrary dimension. Using this, we then show that any metric perturbation of a embedded $n$-sphere is also…

In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth…

We show that immersed minimal surfaces of $\mathbb{R}^{3}$ with bounded curvature and proper self intersections are proper. We also show that the restriction of the immersing map to a wide component is always proper. When the immersing map…

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the…

Performing a computer experiment can be viewed as observing a mapping between the model parameters and the corresponding model outputs predicted by the computer model. In view of this, experimental design for computer experiments can be…

In this paper we study the problem of existence of a crossing-free acyclic hamiltonian path completion (for short, HP-completion) set for embedded upward planar digraphs. In the context of book embeddings, this question becomes: given an…

Mapping a triangulated surface to 2D space (or a tetrahedral mesh to 3D space) is the most fundamental problem in geometry processing.In computational physics, untangling plays an important role in mesh generation: it takes a mesh as an…

Consider an oriented curve $\Gamma$ in a domain $D$ in the plane $\boldsymbol R^2$. Thinking of $D$ as a piece of paper, one can make a curved folding in the Euclidean space $\boldsymbol R^3$. This can be expressed as the image of an…

This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the setting of $(r,\delta)$-convex spaces, a class of geodesic…

Let S be a surface obtained from a plane polygon by identifying infinitely many pairs of segments along its boundary. A condition is given under which the complex structure in the interior of the polygon extends uniquely across the quotient…

We introduce a natural notion of depth that applies to individual cutting planes as well as entire families. This depth has nice properties that make it easy to work with theoretically, and we argue that it is a good proxy for the practical…