Paper preserves properties of mappings through generic mappings.
problem Preserving properties of mappings in higher dimensions.
method Composing generic generalized distance-squared mappings.
result Non-singular or injective properties preserved.
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48 results for “map property”
Extends p-harmonic map theory for new properties.
problem No specific problem stated; extends existing theory.
method Extended p-harmonic and biharmonic map definitions.
result New properties of generalized stable p-harmonic maps.
Digital Shy Mapsmath.GT
Study shy maps in digital topology.
problem Properties of shy maps in digital topology.
method Study properties of shy maps.
result Properties of shy maps in digital topology.
The paper explores the twisted Rokhlin property in mapping class groups of surfaces.
problem Classifying surfaces whose mapping class groups have the twisted Rokhlin property.
method Generalizing the Rokhlin property to the twisted version, the authors classify surfaces based on their mapping class groups' properties.
result The mapping class groups of connected orientable infinite-type surfaces without boundaries have the twisted Rokhlin property, while those of other surfaces do not.
Study proves neck properties for smooth maps with bounded energy.
problem Understanding neck formation in smooth maps with bounded energy.
method Proved energy identity and no neck property for extrinsic polyharmonic maps.
result Established neck properties for maps with bounded total energy.
Investigates maps and properties in spaces with negative dimensions and curvature.
problem Existence of transport maps and local-to-global property in spaces with negative dimensions and bounded Ricci curvature.
method Examines metric measure spaces with negative curvature dimensions and applies reduced curvature-dimension conditions.
result Establishes the existence of transport maps and proves the local-to-global property.
Proves properties of sub-Riemannian exponential map, showing it's not injective.
problem Regularity and continuity of sub-Riemannian exponential map.
method Used sub-Riemannian Jacobi fields and Maslov index of Jacobi curves.
result Exponential map of 3D Heisenberg group is not injective near conjugate vectors.
Proves congruence subgroup property for mapping class groups of hyperbolic surfaces.
problem Residual finiteness of hyperbolic groups and congruence subgroup property for mapping class groups.
method Assumption of residual finiteness of hyperbolic groups leads to proof of congruence subgroup property.
result Congruence subgroup property for mapping class groups of hyperbolic surfaces.
The paper extends a measure preserving property to bi-Lipschitz maps between Moran sets.
problem Extending the measure preserving property to Moran sets.
method Analyzing bi-Lipschitz maps between Moran sets.
result Bi-Lipschitz maps between Moran sets preserve measure locally.
Abstracts a theorem for non-smooth maps in infinite dimensions.
problem Generalizing inverse mapping theorem for non-smooth maps.
method Introduces property A and applies it to non-smooth maps.
result Generalized inverse mapping theorems for non-smooth maps.
Paper proves energy identity and no-neck property for special harmonic maps.
problem Analyzing special harmonic maps with homogeneous targets.
method Introduced equivariant embedding for -harmonic case.
result Energy identity and no-neck property established for - and -harmonic maps.
Cofrontalsmath.DG
Introduces cofrontal mappings and studies their properties.
problem Understanding the properties and behavior of cofrontal mappings.
method Study of cofrontal mappings' local and global properties, construction of fair cofrontals, and classification.
result Cofrontal mappings are very special and restrictive, but can be approximated by fair ones.
Explains mapping properties of elliptic operators in conical spaces.
problem Understanding mapping properties of geometric elliptic operators in conical spaces.
method Develops an approach based on B.-W. Schulze's work.
result Illustrates versatility of results in Geometric Analysis.
Harmonic map flow's singularity properties proven with Lojasiewicz inequalities.
problem Finite-time singularities of harmonic map flow in critical dimensions.
method Proving a weighted Lojasiewicz inequality.
result Continuity of body map and no-neck property for bubble-tree decompositions.
Heat flow method proves existence of harmonic maps.
problem Analyzing harmonic maps from surfaces coupled to potentials.
method Heat flow method
result Existence of critical points in string theory.
Degree theory for orbifoldsmath.GT
Develops degree theory for orbifolds, a generalization of differential topology.
problem No suitable problem statement as the abstract focuses on the development of theory.
method Defined a mapping degree for proper maps between orbifolds, satisfying invariance properties.
result The mapping degree counts preimages of regular values with appropriate weights.
New property for pseudo-Anosov maps and their mapping tori.
problem Understanding pseudo-Anosov maps and their mapping tori.
method Analyzing finite covers and spectral radii of homology actions.
result Monodromy properties of pseudo-Anosov maps' covers.
We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory a…
Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of smoothly local properties. In realising the definition of a local property at a pa…
Fixed points of n-valued maps on surfaces and the Wecken property -- a configuration space approachmath.GT
The paper explores fixed points of n-valued maps on surfaces using configuration spaces.
problem The Wecken property and computation of Nielsen numbers for n-valued maps.
method Configuration spaces and braid groups.
result The projective plane and 2-sphere have the Wecken property for n-valued maps.
Study on finiteness properties of handlebody mapping class groups.
problem Understanding finiteness properties of asymptotically rigid handlebody groups.
method Introduced asymptotically rigid mapping class groups and determined their finiteness properties based on the space of ends of handlebodies.
result Homology of these groups coincides with stable homology of handlebody groups in some cases.
Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.
problem Understanding the properties of two-component bivariate normal mixtures.
method Classification via -equivalence and statistical analysis.
result Three distinct types of mappings with specific geometric and statistical properties, and upper bounds for the number of modes.
Paper generalizes Schwarz Lemma for VT harmonic maps with conditions.
problem Generalizing Schwarz Lemma for a specific type of harmonic maps.
method Conditions on eigenvalues and Ricci curvature are used to prove the lemma.
result Schwarz Lemma for VT harmonic maps proved with distance and volume decreasing properties.
Investigates how adding a scalar potential affects Dirac-harmonic maps.
problem Analyzing the impact of scalar potential on Dirac-harmonic maps.
method Examines various geometric and analytic properties with different potentials.
result Cannot achieve certain properties with the potential term in general.
The study proves unique path lifting properties and their implications on quotient spaces and covering maps.
problem Understanding unique path lifting properties and their implications on quotient spaces and covering maps.
method The study uses group actions on -trees and path lifting properties to prove the main results.
result Every map of manifolds with the unique path lifting property is a covering map.
We study generalized moment maps for a Hamiltonian action on a connected compact -twisted generalized complex manifold introduced by Lin and Tolman and prove the convexity and connectedness properties of the generalized moment maps for a Hamiltonian torus action.
Introduces Hurewicz fibrations for embedding maps of orbifold charts.
problem No specific problem stated; focuses on new concept definition.
method Defines E-fibration embedding and studies its properties.
result Introduces and studies properties of E-fibration embedding.
Sharp mapping properties and regularization for X-ray transform on disks of constant curvature.
problem Sharp mapping properties and regularization of X-ray transform.
method Derive functional relations and mapping properties using elliptic differential operators.
result Theoretical possibility of regularized inversions for X-ray transform.
Study on mapping class groups of infinite type surfaces.
problem Property for mapping class groups of infinite type surfaces.
method Analyzes the existence of elements and satisfying specific group properties.
result Establishes the existence of for any finite collection of non-trivial elements .
Congruence Subgroup Property for nilpotent groups and subsurface subgroups of Mapping Class Groupsmath.GR
Proves Congruence Subgroup Property for two types of groups.
problem Proving Congruence Subgroup Property for specific groups.
method Elementary proof of Johnson filtration and geometric subsurface inclusions.
result Proves Congruence Subgroup Property for nilpotent quotients and subsurface subgroups.
Study shows conjugacy of torsion in genus 2 surfaces.
problem Torsion elements in mapping class groups of surfaces.
method Proved congruence subgroup property for centralizers of finite subgroups.
result Torsion elements in surfaces of genus ≤ 2 are conjugacy distinguished.
We prove that the mapping class group of a closed oriented surface of genus at least two does not have Kazhdan's property (T).
Study big mapping class groups and their co-Hopfian property, finding new examples and proving injective homomorphisms results.
problem Characterizing co-Hopfian property in big mapping class groups of infinite-type surfaces.
method Constructing examples, proving properties, exploring injective homomorphisms.
result First examples of injective endomorphisms of mapping class groups of infinite-type surfaces that fail to be surjective.
The article studies mapping properties of Radon transform and backprojection on a unit ball.
problem Polyhomogeneous mapping properties of Radon transform and backprojection operator on the unit ball.
method Constructs a double b-fibration to desingularize the point-hyperplane relation, provides formulas and sharper estimates.
result Sharper estimates on polyhomogeneous mapping properties of Radon transform and backprojection compared to classic estimates.
Study maps in semidirect products of groups, proving Lipschitz properties without intrinsic dilations.
problem Proving Lipschitz conditions in semidirect products of groups without intrinsic dilations.
method Using equivalent conditions and properties of projection maps in metric spaces.
result Proves the same Lipschitz results as in Carnot groups, without intrinsic dilations.
Investigates properties of moment maps and stratifications on Lie groups.
problem Understanding moment maps and stratifications on real reductive Lie groups.
method Functorial, algebraic approach to moment map and Kirwan-Ness stratification.
result Properties and properties of moment maps and stratifications established.
Survey on random walks on mapping class groups and their properties.
problem Understanding random walks on mapping class groups.
method Analyzing actions on Teichmüller spaces and curve complexes.
result Laws of large numbers and central limit theorems for random walks.
New stretch maps minimize distortion in geometric group theory.
problem Finding optimal maps in geometric group theory.
method Proving minimizers using modulus of curve families and MSP.
result Stretch maps are minimizers of mean quasiconformal distortion.
Discussing rigidity properties of conics, inspired by billiards in ellipses.
problem Rigidity properties of conics and billiards in ellipses.
method Analog of polar duality and circle map properties.
result Two rigidity properties of conics.
Study analyzes convergence of harmonic maps into compact locally CAT(1) spaces.
problem Analyzing convergence of harmonic maps with energy bounds.
method Bubble tree convergence, exploiting local convexity properties of CAT(1) spaces.
result Energy quantization and no-neck property demonstrated for harmonic maps.
We provide a general framework to study convergence properties of families of maps. For manifolds and where is equipped with a volume form we consider families of maps in the collection and we define a distance function …
Study on singularities of Gauss maps of wave fronts with specific properties.
problem Characterizing singularities of Gauss maps of wave fronts.
method Geometric properties and boundedness of Gaussian curvatures.
result Relation between boundedness of Gaussian curvatures and types of singularities of Gauss maps.
In this article, we prove a Liouville property of holomorphic maps from a complete Kahler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kahler manifold with a certain assumption on the sectional curvature.
The paper connects moment maps to the stability of holomorphic fibrations.
problem Stability of holomorphic fibrations.
method Use of moment maps and K-stability criteria.
result Existence of optimal symplectic connections implies stability of fibrations.
Study convexity properties of gradient map on probability measures.
problem Properties of gradient map on probability measures on submanifolds.
method Analysis of Kähler manifolds and Lie group actions.
result Convexity results for gradient map in Abelian case, extension to non-Abelian case.
Study modular classes of Dirac manifolds and maps, explaining their properties and relationships.
problem Exploring modular classes of Dirac structures and their relationships.
method Analysis of modular classes, properties derivation, and relationship explanation.
result Explains the relationship between modular classes of various structures in Poisson reduction.
Introduces generalized moment maps for almost Hermitian settings.
problem Extending classical moment map theory to almost Hermitian settings.
method Introduces momentumly closed forms and proves a variant of the Darboux-Weinstein theorem.
result Establishes convexity property and constructs reduction space for generalized moment maps.
We explore the intrinsic geometry of tangent bundles and properties of the mirror map.
problem Understanding the intrinsic geometry of tangent bundles and properties of the mirror map.
method Review and solve cohomological questions related to the mirror map and related operators.
result Solved some cohomological questions and raised other induced by the d_B operator.