We consider harmonic diffeomorphisms to a fixed hyperbolic target , from a family of domain Riemann surfaces degenerating along a Teichmüller ray. We use the work of Minsky to show that there is a limiting harmonic map from the conformal limit of the Teichmüller ray, to a crowned hyperbolic surface. The target surfa…
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48 results for “crowned hyperbolic surfaces”
Study on anti-de Sitter structures on surfaces with punctures.
problem Deformation of anti-de Sitter structures on surfaces with punctures.
method Parameterization of deformation space using Teichmüller spaces and quadratic differentials.
result Two parameterizations of the deformation space of wild globally hyperbolic anti-de Sitter structures.
We use meromorphic quadratic differentials with higher order poles to parametrize the Teichmüller space of crowned hyperbolic surfaces. Such a surface is obtained on uniformizing a compact Riemann surface with marked points on its boundary components, and has non-compact ends with boundary cusps. This extends Wolf's pa…
This paper studies deformations of hyperbolic surfaces with special structures.
problem Infinitesimal deformations of hyperbolic surfaces with boundary and ideal vertices.
method Description of the admissible cone of deformations in terms of the arc complex.
result Realization of the admissible cone and its faces as arc complexes for specific surface families.
Mirzakhani volumes of moduli spaces are polylogarithmic.
problem Understanding the volume of moduli spaces of hyperbolic surfaces.
method Expressed as a sum of polylogarithms evaluated at specific points.
result Mirzakhani volumes are polylogarithmic.
Paper simplifies proof of slide-equivalence in crown diagrams.
problem Proving slide-equivalence of crown diagrams.
method Diagrammatic approach to generalized shift moves.
result Slide-equivalence of vanishing cycles in crown diagrams.
The paper proves a grafting theorem for meromorphic projective structures and shows the monodromy map is a local homeomorphism.
problem Understanding projective structures on Riemann surfaces with poles.
method Proves a grafting theorem involving crowned hyperbolic surfaces and uses the monodromy map to a decorated character variety.
result The monodromy map to the decorated character variety is a local homeomorphism.
Efficiently verifies neural networks by handling neuron splits, improving speed and accuracy.
problem Handling neuron split constraints in incomplete neural network verification.
method β-CROWN, which optimizes parameters β to encode neuron splits and uses them in bound propagation.
result β-CROWN significantly speeds up verification while maintaining high accuracy.
Paper examines 4-manifold structures using chord assignments.
problem Determining if knot surgery 4-manifolds are diffeomorphic.
method Assigns integers to chords in crown diagrams to compare smooth structures.
result Smooth structures on knot surgery 4-manifolds are not isotopic.
New method CROWN-IBP combines IBP and CROWN for efficient verifiable robust neural networks.
problem Training verifiably robust neural networks is challenging and computationally expensive.
method CROWN-IBP combines interval bound propagation and linear relaxation for efficient training.
result CROWN-IBP achieves significant improvements in verifiable robustness on MNIST and CIFAR datasets.
CROWN certifies robustness of neural networks with general activation functions.
problem Certifying robustness of neural networks with general activation functions.
method Bounding activation functions with linear and quadratic surrogates, adaptively selecting surrogates for each neuron.
result Significantly improves certified lower bounds on ReLU networks compared to Fast-Lin.
Let be the crown domain associated with a non-compact irreducible hermitian symmetric space . We give an explicit description of the unique -invariant adapted hyper-Kähler structure on ,i.e.compatible with the adapted complex structure and with the -invariant Kähle…
A Morse 2-function is a generic smooth map from a manifold M of arbitrary finite dimension to a surface B. Its critical set maps to an immersed collection of cusped arcs in B. The aim of this paper is to explain exactly when it is possible to move these arcs around in B by a homotopy and to give a library of examples w…
Generalizes neural network verification by adding arbitrary cutting planes.
problem Handling general cutting plane constraints in neural network verification.
method Generalized bound propagation method (GCP-CROWN) that allows arbitrary cutting plane constraints.
result GCP-CROWN significantly improves neural network verification performance.
SLIC-UAV monitors forest recovery using UAVs and machine learning.
problem Challenges in monitoring forest recovery, especially in logged tropical forests.
method Novel pipeline for UAV imagery analysis, combining crown labelling, species classification, and superpixel segmentation.
result SLIC-UAV achieves high accuracy in species mapping, from 79.3% to 90.5%.
The paper analyzes constrained optimal portfolios in high dimensions using novel statistical learning techniques.
problem Forming optimal portfolios with constraints in high-dimensional asset spaces.
method CROWN method integrating factor models with nodewise regression for estimation in large dimensions.
result Demonstrates estimation consistency and convergence rates for constrained portfolio weights, risk, and Sharpe Ratio.
We study the profitability of optimal mean reversion trading strategies in the US equity market. Different from regular pair trading practice, we apply maximum likelihood method to construct the optimal static pairs trading portfolio that best fits the Ornstein-Uhlenbeck process, and rigorously estimate the parameters.…
FROWN optimizes neural network robustness, improving safety in deep learning.
problem Ensuring robustness of neural networks against adversarial attacks.
method Optimization-based approach to tighten robustness certificates.
result Deterministic CROWN solutions are optimal under mild constraints.
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.
Introduces Möbius structures and hyperbolic ends for -surfaces in hyperbolic space.
problem Understanding -surfaces in hyperbolic space.
method Studies Möbius structures and hyperbolic ends.
result Applications to -surfaces in hyperbolic space.
Study of hyperbolic polyhedral surfaces with regular faces.
problem Understanding the properties of hyperbolic polyhedral surfaces with regular faces.
method Combinatorial and geometric analysis of hyperbolic polyhedral surfaces with regular faces.
result There is a gap between the areas of non-smooth hyperbolic polyhedral surfaces and smooth hyperbolic surfaces.
Geodesic surfaces embed into hyperbolic 3-manifolds for all finite group actions.
problem Embedding geodesic surfaces into hyperbolic 3-manifolds.
method Analyzing finite group actions on surfaces and proving geodesic embeddings for all irreducible cases.
result All quasiplatonic surfaces embed geodesically into hyperbolic 3-manifolds.
SAWAR improves SA models by making them more robust to data uncertainties.
problem Improving survival analysis models' robustness to data uncertainties.
method Adversarial robustness through Min-Max optimization with CROWN-IBP.
result SAWAR outperforms baseline methods and SOTA models across various metrics.
Algorithm morphs graphs on hyperbolic surfaces.
problem Morphing graphs on hyperbolic surfaces.
method Generalization of Tutte's spring embedding theorem.
result First algorithm for morphing graphs on hyperbolic surfaces.
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.
The study classifies timelike meridian surfaces in Minkowski 4-space.
problem Characterizing timelike meridian surfaces in Minkowski space.
method Analyzing surfaces as one-parameter systems of meridians of rotational hypersurfaces.
result Classification of timelike meridian surfaces with various curvature properties.
Bounding shears in ideal triangulations on hyperbolic surfaces.
problem Bounding shears in ideal triangulations on hyperbolic surfaces.
method Showing an ideal triangulation with bounded shear parameters on hyperbolic surfaces.
result An upper bound on shear parameters depends logarithmically on the surface's topology.
Classifies hyperbolic groups with surface-like boundaries.
problem Classifying hyperbolic groups with specific surface-like boundaries.
method Analyzing quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.
result Identifies hyperbolic groups with surface-like boundaries.
The study characterizes quasiperiodic surfaces in pseudo-hyperbolic spaces with curvature conditions.
problem Characterizing quasiperiodic surfaces in pseudo-hyperbolic spaces.
method Curvature conditions, Gromov hyperbolicity, conformal hyperbolicity.
result Limit curves of quasiperiodic surfaces in the Einstein Universe have canonical quasisymmetric parametrizations.
Infinite-genus surfaces have many isospectral hyperbolic structures.
problem Finding many isospectral hyperbolic structures on infinite-genus surfaces.
method Constructing families of isospectral hyperbolic structures on infinite-type surfaces without planar ends.
result Uncountable families of isospectral and quasiconformally distinct hyperbolic structures on infinite-genus surfaces with self-similar end spaces.
Hensel-Przytycki-Webb proved that all curve graphs of orientable surfaces are 17-hyperbolic. In this paper, we show that curve graphs of non-orientable surfaces are 17-hyperbolic by applying Hensel-Przytycki-Webb's argument. We also show that arc graphs of non-orientable surfaces are 7-hyperbolic, and arc-curve graphs …
Graded identities for hyperbolic surfaces with cusps and cone points.
problem Understanding dilogarithm identities on hyperbolic surfaces.
method Establishing graded versions of Bridgeman's dilogarithm identity.
result Applications to the study of orthogeodesics.
Minimal Delaunay triangulations on hyperbolic surfaces have linear number of vertices.
problem Finding the minimum number of vertices in Delaunay triangulations of hyperbolic surfaces.
method Analyzing the genus of hyperbolic surfaces to derive bounds on the number of vertices.
result The number of vertices in minimal Delaunay triangulations of hyperbolic surfaces is linear in the genus .
The paper proves smooth minimal surfaces in hyperbolic 3-manifolds.
problem Existence of smoothly embedded minimal surfaces in hyperbolic 3-manifolds.
method Analytical proof in hyperbolic geometry.
result Existence of smoothly embedded closed minimal surfaces in hyperbolic 3-manifolds.
Unstable minimal surfaces in n-space link to hyperbolic products.
problem Characterizing unstable minimal surfaces in and their product counterparts.
method Lifting to -trees, deforming to hyperbolic products, and proving instability equivalence.
result Unstable minimal surfaces in imply unstable surfaces in product hyperbolic spaces.
Study on embedding surfaces into 3-manifolds, focusing on equivariant cases.
problem Embedding hyperbolic surfaces into hyperbolic 3-manifolds with specific symmetries.
method Examined orientation-preserving and orientation-reversing actions on surfaces, including nonorientable ones.
result Found conditions for equivariant embeddings of hyperbolic surfaces into hyperbolic 3-manifolds.
Paper finds shortest geodesic paths on hyperbolic surfaces.
problem Finding the shortest geodesic paths on hyperbolic surfaces.
method Analyzes genus g hyperbolic surfaces to find minimal length geodesics.
result Minimal geodesic length is realized by a specific polygon.
Shortest non-simple closed geodesics on hyperbolic surfaces found.
problem Finding the shortest non-simple closed geodesics on hyperbolic surfaces.
method Analyzing closed geodesics with at least k self-intersections on hyperbolic surfaces.
result The shortest non-simple closed geodesics lie on an ideal pair of pants and have length $2\arccosh(2k+1)$.
Paper studies flow on hyperbolic surfaces to match boundary lengths.
problem Matching boundary lengths of hyperbolic surfaces.
method Combinatorial Yamabe flow on hyperbolic bordered surfaces.
result Flow converges exponentially to a surface with equal boundary lengths.
Survey on spectral gaps of random hyperbolic surfaces.
problem Understanding spectral gaps of random hyperbolic surfaces.
method Brief survey on geometry and spectra, discussion of results by Hide-Magee, Anantharaman-Monk, and Hide-Macera-Thomas.
result Near optimal spectral gaps for random surfaces.
Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.
problem Finding optimal discrete harmonic maps between hyperbolic surfaces.
method Minimizing Dirichlet energy over all possible hyperbolic structures and realizations within a fixed homotopy class.
result At the optimal hyperbolic structure, the discrete harmonic map and edge weights are induced from a weighted Delaunay decomposition.
Random hyperbolic surfaces have low Cheeger constants.
problem Estimating Cheeger constants of random hyperbolic surfaces.
method Modeling random hyperbolic surfaces using ideal triangles and analyzing their Cheeger constants.
result Generic hyperbolic surfaces have Cheeger constants less than 3/2π + ε.
Groups satisfy linear surface isoperimetric functions.
problem Isoperimetric functions for surface diagrams in hyperbolic groups.
method Analyzing word-hyperbolic groups and their surface diagrams.
result Linear isoperimetric functions for all surface types in hyperbolic groups.
Polyhedral surfaces in flat (2+1)-spacetimes and balanced cellulations on hyperbolic surfacesmath.MG
Flat metrics on hyperbolic surfaces embed as polyhedral surfaces in (2+1)-spacetimes.
problem Embedding flat metrics on hyperbolic surfaces into (2+1)-spacetimes.
method Using convex polyhedral Cauchy surfaces and Teichmüller space properties.
result Existence and uniqueness of flat metrics embedding in (2+1)-spacetimes.
Bi-geodesic mappings preserve distances on hyperbolic surfaces with boundaries.
problem Preserving distances on hyperbolic surfaces with boundaries.
method Proving bijections between geodesics are isometries.
result A bijection between geodesics is an isometry.
The cost of belief changes with precision and is a hyperbolic geometry.
problem The cost of belief changes with precision and is a hyperbolic geometry.
method The cost of belief changes with precision and is a hyperbolic geometry.
result The cost of belief changes with precision and is a hyperbolic geometry.
Study finds limit points of bass notes on hyperbolic surfaces.
problem Understanding the limit points of bass notes on hyperbolic surfaces.
method Proved using mathematical analysis of arithmetic hyperbolic surfaces.
result Limit points are found to be within the interval [0, 1/4].
New construction of minimal surfaces in hyperbolic space.
problem Creating minimal surfaces with specific properties in hyperbolic space.
method Presented a new construction method.
result Embedded minimal surfaces with 3 asymptotically totally geodesic ends and arbitrary finite genus.