Paper proves C0-semi-rigidity of meandering-hyperbolic actions.
problem Stability of meandering-hyperbolic actions in C0 topology. method Proves semi-rigidity using local C0-semi-rigidity. result Every meandering-hyperbolic action is locally semi-rigid in C0 topology. In his 1985 paper Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and introduce a notion of "meandering hyperbolicity" for group actions on geodesic metric spaces. This generalizati…
New model for links uses meander diagrams and combinatorics.
problem Modeling and analyzing random links.
method Random meander model based on meander diagrams and graphs, proving properties using combinatorics.
result Trivial links are unlikely, and there's a lower bound on non-isotopic knots.
We introduced concept of meander knots, 2-component meander links and multi-component meander links and derived different families of meander knots and links from open meanders with at most 16 crossings. We also defined semi-meander knots (or knots with ordered Gauss code) and their product.
Study bounds growth rate of irreducible meanders, showing proportion vanishes.
problem Understanding growth rate of irreducible meanders.
method Provided upper and lower bounds for growth rate.
result Proportion of irreducible meanders among prime meanders approaches 0 as n increases.
Study on a new class of meanders with tangential intersections.
problem Enumerating and understanding meanders with transverse intersections.
method Developed a combinatorial framework, identified connections with other objects, and enumerated specific families.
result Completely enumerated several families of singular meanders.
Generalizes meander diagrams to virtual knots and introduces new invariants.
problem Classifying and comparing virtual knots.
method Generalization of meander diagrams to virtual knots, introduction of virtual k-arc crossing numbers. result Classes of meander and semimeander diagrams are universal for virtual knots.
Resolving Schwartz's quadratic meander number conjecture
problem Meander number of cyclic permutations
method Constructing families of cyclic permutations
result Meander number is bounded above and below quadratically in n
Counting meanders on surfaces of arbitrary genus, with precise asymptotics.
problem Counting and understanding meanders on surfaces of arbitrary genus.
method Square-tiled surfaces, moduli spaces of Abelian and quadratic differentials, Witten-Kontsevich 2-correlators.
result Asymptotic probability and polynomial growth of meanders with intersections.
A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincaré and naturally appear in various areas of mathematics, theoretical physics and computational biology (in par…
A meander of order n is a simple closed curve in the plane which intersects a horizontal line transversely at 2n points. (Meanders which differ by an isotopy of the line and plane are considered equivalent.) Let Gamma_n be the Cayley graph of the symmetric group S_n as generated by all (n choose 2) transpositions. Let …
Minimal constructions of meanders and hyperelliptic pillowcase covers help in understanding ratio-optimizing pseudo-Anosovs.
problem Understanding ratio-optimizing pseudo-Anosovs in moduli spaces of quadratic differentials.
method Minimal constructions of meanders and hyperelliptic pillowcase covers.
result Existence of ratio-optimizing pseudo-Anosovs deep in the Johnson filtration.
We found a way to code meanders and show they are idempotent.
problem Understanding and coding meandric permutations.
method We established a bijection between meanders and Gauss diagrams, and used this to construct matrices that are idempotent.
result Meandric permutations are idempotent over the field GF(2).
New estimate of semimeander complexity for knots with more than 10 crossings.
problem Estimating the complexity of semimeander diagrams of knots.
method Proved a new upper bound on the number of crossings for semimeander diagrams of knots with more than 10 crossings.
result For knots with more than 10 crossings, semimeander diagrams have no more than 0.31⋅1.558cr(K) crossings. We study decomposition into simple arcs (i. e., arcs without self-intersections) for diagrams of knots and spatial graphs. In this paper, it is proved in particular that if no edge of a finite spatial graph G is a knotted loop, then there exists a plane diagram D of G such that (i) each edge of G is represented…
The problem of which Gauss diagram can be realized by plane curves is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. We show that needed conditions for realizability of a Gauss diagram can be interpreted as follows "the number of exits = the number of entran…
We propose a simple stochastic model for the dynamics of a limit order book, extending the recent work of Cont and de Larrard (2013), where the price dynamics are endogenous, resulting from market transactions. We also show that the conditional diffusion limit of the price process is the so-called Brownian meander.
We study collections of planar curves that yield diagrams for all knots. In particular, we show that a very special class called potholder curves carries all knots. This has implications for realizing all knots and links as special types of meanders and braids. We also introduce and apply a method to compare the effici…
This note re-addresses the Paris barrier options proposed by Yor and collaborators and their valuation using the Laplace transform approach. The notion of Paris barrier options, based on excursion theory and using the Brownian meander, is extended such that their valuation is now possible at any point during their life…
The paper examines circle graphs of Gauss diagrams and finds counterexamples to previous descriptions.
problem Problems with previous descriptions of realizable Gauss diagrams.
method Experimental checking and formulation of new descriptions of realizable circle graphs.
result New descriptions of realizable circle graphs and an algorithm for checking realizability.
Jablan and Radović originally defined two invariants called the Meander number and OGC number of knots for certain classes of knots. We generalize these definitions to all knots and name the straight number and contained straight number of a knot, respectively, and prove they are well defined. We answer two questions a…
Paper presents a GAN model for realistic river image synthesis.
problem Generating high-quality river images for hydrological research.
method Used a Progressive Growing GAN (PGGAN) architecture to overcome training challenges.
result Demonstrated the effectiveness of GANs in generating high-resolution river images.
Investigates Q value evolution in Stable Baselines for DQL in simple vs complex environments.
problem DQL in Stable Baselines struggles with simple non-game environments.
method Comparison of TrafficLight and FrozenLake environments; Q value decomposition analysis.
result Q values meander far from optimal in complex relationships between states.
Study uses DMD to analyze oceanic features in Strait of Gibraltar.
problem Understanding complex oceanic features in Strait of Gibraltar.
method Dynamic Mode Decomposition (DMD) applied to 3D MIT general circulation model simulations.
result Unveiled new elements and dynamics of the Strait of Gibraltar, including a secondary gyre and wave propagation.
New hyperbolicity concepts expand manifold study.
problem Studying hyperbolicity on complex manifolds.
method Introducing sG-hyperbolicity, weakly p-Kähler hyperbolic structures, and pluriclosed star split hyperbolic metrics.
result Expands the class of divisorially hyperbolic manifolds.
The paper defines two types of hyperbolicity for complex manifolds and proves related results.
problem Defining and studying hyperbolicity for a broader class of complex manifolds.
method Introducing SKT hyperbolicity and Gauduchon hyperbolicity, proving results using SKT and Gauduchon metrics.
result Every SKT hyperbolic manifold is also Kobayashi/Brody hyperbolic and every Gauduchon hyperbolic manifold is divisorially hyperbolic.
New criteria for relative hyperbolicity in hierarchically hyperbolic spaces.
problem Characterizing relative hyperbolicity in hierarchically hyperbolic spaces.
method New formulation of relative hyperbolicity in terms of hierarchy structures, applied to graphs associated to surfaces.
result The separating curve graph of a surface is relatively hyperbolic when the surface has zero or two punctures.
Introduces Möbius structures and hyperbolic ends for k-surfaces in hyperbolic space.
problem Understanding k-surfaces in hyperbolic space. method Studies Möbius structures and hyperbolic ends.
result Applications to k-surfaces in hyperbolic space. Introduces hyperbolic generalized framed surfaces and their properties.
problem None explicitly stated; focuses on introducing new geometric objects.
method Generalization of hyperbolic framed surfaces and curves.
result Established conditions for a surface to be a hyperbolic generalized framed base surface and explored their singularities.
Study on new hyperbolicity notions for non-Kähler manifolds and their deformations.
problem Analyzing new hyperbolicity notions for non-Kähler complex manifolds.
method Introducing and analyzing two new notions of hyperbolicity for compact complex non-Kähler manifolds, and studying their behavior under smooth modifications.
result Established openness results for p-HS hyperbolicity and p-Kähler hyperbolicity under holomorphic deformations. New formulas for hyperbolic mass using horospheres.
problem Mass calculation of asymptotically hyperbolic manifolds.
method Geometric formulas derived using coordinate horospheres.
result Improved rigidity results of hyperbolic space.
Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.
problem Existence of non-residually finite hyperbolic groups
method Direct implication
result Existence of non-residually finite rigid hyperbolic groups
Study complex hyperbolic lattices and their relation to strict hyperbolization.
problem Understanding the relationship between complex hyperbolic lattices and strict hyperbolization.
method Analyzing the fundamental groups of complex hyperbolic manifolds and spaces arising from strict hyperbolization.
result Uniform lattices in PU(n,1) cannot be fundamental groups of Charney-Davis strict hyperbolizations when n ≥ 2.
We study hyperbolic bongles and find their volumes.
problem Characterizing and quantifying hyperbolic bongles.
method Provided necessary and sufficient conditions for hyperbolicity, calculated volumes, and established upper bounds.
result All balanced hyperbolic n-bongles have the same volume and this volume is an upper bound for any hyperbolic n-bongle. Abstract reviews hyperbolic positive energy theorems.
problem Analyzing positive energy theorems for hyperbolic spaces.
method Review of existing literature on asymptotically hyperbolic manifolds.
result Summarizes positive energy theorems for hyperbolic spaces.
Paper finds inequalities for convex domains in hyperbolic space.
problem Finding inequalities for convex domains in hyperbolic space.
method Introducing hyperbolic ellipsoids and using orthogonal projection to establish inequalities.
result Affine isoperimetric inequalities for static convex domains in hyperbolic space characterized by hyperbolic ellipsoids.
We study conservative partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds. We show that they are always accessible and deduce as a result that every conservative C1+ partially hyperbolic in a hyperbolic 3-manifold must be ergodic, giving an afirmative answer to a conjecture of Hertz-Hertz-Ures in the co…
Crochet models show hyperbolic geometry properties.
problem Visualizing hyperbolic geometry concepts.
method Triangulated hyperbolic plane models.
result Demonstrates various hyperbolic geometry properties.
Study deformations of compact Kähler hyperbolic manifolds.
problem Investigate the deformation openness of Kähler hyperbolicity.
method Propose modified versions of Kähler hyperbolicity as a tool.
result Provide a first step towards understanding deformations.
We show that a relatively hyperbolic graph with uniformly hyperbolic peripheral subgraphs is hyperbolic. As an application, we show that the disc graph and the electrified disc graph of a handlebody H of genus g>1 are hyperbolic, and we determine their Gromov boundaries.
Study shows hyperbolic subgroups can be free products of surface and free groups.
problem Characterizing hyperbolic subgroups within larger groups.
method Analyzing fiber bundles and using properties of hyperbolic groups.
result Non-elementary hyperbolic commensurated subgroups are virtually free products of surface and free groups.
New 5D hyperbolic shapes that wrap around a circle found.
problem Finding new 5D hyperbolic structures.
method Examined finite-volume cusped hyperbolic 5-manifolds.
result Discovered the smallest known hyperbolic 5-manifold.
Study properties of hyperbolic Yamabe solitons in submanifolds.
problem Characterize and understand hyperbolic Yamabe solitons in submanifolds.
method Define hyperbolic Yamabe flow, prove properties, and classify solitons.
result Prove that hyperbolic Yamabe solitons are pseudosymmetric or metallic shaped.
Survey solves curvature problems with hyperbolic spaces.
problem Singularities in hypersurface geometry.
method Hyperbolic unfolding correspondence linking hypersurfaces to Gromov hyperbolic spaces.
result Eliminates hypersurface singularities in scalar curvature geometry.
Drilling hyperbolic groups to simplify complex conjectures.
problem Proving the Cannon Conjecture for hyperbolic groups with 2-sphere boundary.
method Defining drilling of hyperbolic groups and proving it preserves relative hyperbolicity.
result Reduction of the Cannon Conjecture to a more tractable relative version.
HKConv learns hyperbolic features by aggregating kernel points.
problem Challenges in learning good hyperbolic representations using Euclidean operations.
method Proposes HKConv, a trainable hyperbolic convolution that correlates local features with kernel points and aggregates them.
result HKConv learns expressive local features according to hyperbolic geometry and enjoys equivariance to permutation and invariance to parallel transport.
Harmonic maps from hyperbolic planes to hyperbolic space exist with given boundary data.
problem Existence of harmonic maps from product of hyperbolic planes to hyperbolic space.
method Existence result for asymptotic Dirichlet problem.
result Existence of harmonic maps with given boundary data.
We show the equivalence of several characterizations of relative hyperbolicity for metric spaces, and obtain extra information about geodesics in a relatively hyperbolic space. We apply this to characterize hyperbolically embedded subgroups in terms of nice actions on (relatively) hyperbolic spaces. We also study the d…