arXiv research

Ends and cohomology theory for noncompact spaces.

New insights into ends of quotient spaces and graphs.

New Hilbert bundles with ends defined from indexed bases.

Two results on end spaces of infinite type surfaces, answering questions about their topology and equivalence.

Introduces Möbius structures and hyperbolic ends for $k$-surfaces in hyperbolic space.

In this paper we consider the conformal type (parabolicity or non-parabolicity) of complete ends of revolution immersed in simply connected space forms of constant sectional curvature. We show that any complete end of revolution in the $3$-dimensional Euclidean space or in the $3$-dimensional sphere is parabolic. In th…

We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is an ``elliptic end'' (resp. a ``hyperbolic end'') if the monodromy matrix at the …

Study of non-metrizable manifolds' ends, generalizing Nyikos's theorem.

The paper extends end concepts to arbitrary groups and spaces.

Unified proof of end-point estimates for Radon transform on curved spaces.

We show that an Osserman-type inequality holds for spacelike surfaces of constant mean curvature (CMC) 1 with singularities and with elliptic ends in de Sitter 3-space. An immersed end of a CMC 1 surface is an ``elliptic end'' if the monodromy representation at the end is diagonalizable with eigenvalues in the unit cir…

Uniform bounds on ends for non-branching CD spaces with nonnegative curvature outside a compact set.

Paper defines end Khovanov homology to detect exotic planes.

There is a well-known correspondence between infinite trees and ultrametric spaces which can be interpreted as an equivalence of categories and comes from considering the end space of the tree. In this equivalence, uniformly continuous maps between the end spaces are translated to some classes of coarse maps (or even c…

Theory of ends of spaces using linear algebra.

Using Traizet's regeneration method, we prove that for each positive integer n there is a family of embedded, doubly periodic minimal surfaces with parallel ends in Euclidean space of genus 2n-1 and 4 ends in the quotient by the maximal group of translations. The genus 2n-1 family converges smoothly to 2n copies of Sch…

We prove that the ending lamination space of the five-punctured sphere is homeomorphic to the Noebeling curve.

New method constructs surfaces with constant mean curvature.

New metrics with constant Q-curvature created by gluing.

The paper sets limits on the number of ends of certain geometric structures.

The study explores ends in coarse homotopy of proper geodesic spaces.

The paper constructs surfaces of high genus with three ends.

We compute the flux of Killing fields through ends of constant mean curvature 1 in hyperbolic space, and we prove a result conjectured by Rossman, Umehara and Yamada : the flux matrix they have defined is equivalent to the flux of Killing fields. We next give a geometric description of embedded ends of finite total cur…

Groups acting on bifoliated planes are left-orderable.

A local deformation property for uniform embeddings in metric manifolds (LD) is formulated and its behaviour is studied in a formal view point. It is shown that any metric manifold with a geometric group action, typical metric spaces (Euclidean space, hyperbolic space and cylinders) and for κ\leq 0 the κ-cone ends over…

In this paper, we study the PSV construction, which provides a step by step method for obtaining tame translation surfaces with a suitable Veech group. In addition, we modify slightly this construction, and for each finitely generated subgroup $G<{\rm GL}_{+}(2,\mathbb{R})$ without contracting elements, we produce a ta…

Compact moduli space shown for Seiberg-Witten on flat scalar curvature manifold.

Study examines $L^p$-boundedness of Hodge projection on manifolds with ends.

Every connected, weighted graph with non-negative curvature has exactly two ends.

Current machine learning techniques proposed to automatically discover a robot kinematics usually rely on a priori information about the robot's structure, sensors properties or end-effector position. This paper proposes a method to estimate a certain aspect of the forward kinematics model with no such information. An …

We show existence of constant mean curvature 1 surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter 3-space, but with a different non-embedded end behavior.

This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our ma…

NDPs embed dynamical systems into neural networks for efficient sensorimotor learning.

We show that if S is a finite type orientable surface of negative Euler characteristic which is not the 3-holed sphere, 4-holed sphere or 1-holed torus, then the ending lamination space of S is connected, locally path connected and cyclic.

We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We characterize fundamental domains of our \cmc surfaces by associated great circle polyg…

PyODDS automates outlier detection for new data sources.

A novel kernel-based support vector machine (SVM) for graph classification is proposed. The SVM feature space mapping consists of a sequence of graph convolutional layers, which generates a vector space representation for each vertex, followed by a pooling layer which generates a reproducing kernel Hilbert space (RKHS)…

In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic 3-space H^3. Galvez, Martinez and Milan showed that when the singular set does not accumulate at an end, the end is asymptotic to a rotationally symmetric flat surface. As a refinement of their result, we show that …

We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.

New exotic 4D spaces found using knot slicing techniques.

Finite graphs with specific curvature have limited harmonic functions and ends.

For a complete minimal surface in the Euclidean 3-space, the so-called flux vector corresponds to each end. The flux vectors are balanced, i.e., the sum of those over all ends are zero. Consider the following inverse problem: For each balanced n vectors, find an n-end catenoid which attains given vectors as flux. Here,…

In this paper we construct examples of Weil-Petersson geodesics with nonminimal ending laminations which have 1-dimensional limit sets in the Thurston compactification of Teichmüller space.

Veech groups uniformize Teichmüller geodesic curves in Riemann moduli space. Recently, examples of infinitely generated Veech groups have been given. We show that these can even have infinitely many cusps and infinitely many infinite ends. We further show that examples exist for which each direction of an infinite end …

Pixel-space diffusion models outperform latent models on high-resolution image synthesis.

We combine the DPW method and Opening Nodes to construct embedded surfaces of positive constant mean curvature with Delaunay ends in euclidean space, with no limitation to the genus or number of ends.

New theorem bounds group quotient size to subgroups index.

The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.