Maps on torus are Archimedean tilings or quotients of them.
problem Characterize semi-equivelar maps on torus.
method Analyze face-cycles, quotient maps, vertex-transitivity, and orbit counts.
result Each semi-equivelar map on torus is a quotient of an Archimedean tiling.
This paper shows semi-equivelar toroidal maps are vertex-transitive covers.
problem Understanding the relationship between semi-equivelar and vertex-transitive toroidal maps.
method Proving semi-equivelar toroidal maps are quotients of vertex-transitive toroidal maps.
result Each semi-equivelar toroidal map has a finite vertex-transitive cover.
This paper classifies semi-equivelar maps on a special surface.
problem Classifying semi-equivelar maps on a surface of Euler genus 3.
method Analyzing cyclic face sequences and presenting complete map types.
result Complete list of semi-equivelar maps on a surface of Euler characteristic -1.
This paper classifies semi-equivelar maps on torus and Klein bottle with few vertices.
problem Classifying semi-equivelar maps on non-spherical surfaces.
method Analyzing known tilings of the plane to suggest possible types, then classifying maps with few vertices.
result Classification of semi-equivelar maps on torus and Klein bottle with few vertices.
The study identifies 11 types of semi-equivelar maps on the torus, with some being vertex-transitive.
problem Characterizing semi-equivelar maps on the torus and identifying vertex-transitive ones.
method Analysis of automorphism groups and face-cycles.
result There are 11 types of semi-equivelar maps on the torus, with some being vertex-transitive.
New semi-equivelar map found on sphere, not vertex-transitive.
problem Characterizing semi-equivelar maps on sphere.
method Combinatorial proofs and vertex-transitivity analysis.
result Exactly one semi-equivelar map on sphere is not vertex-transitive.
Semi-Equivelar maps are generalizations of Archimedean Solids (as are equivelar maps of the Platonic solids) to the surfaces other than 2−Sphere. We classify some semi equivelar maps on surface of Euler characteristic -1 and show that none of these are vertex transitive. We establish existence of 12-covered triangula…
Hamiltonian cycles found in toroidal maps.
problem Hamiltonicity of doubly semi-equivelar maps on the torus.
method Analyzing 2-uniform tilings of the plane to derive Hamiltonian cycles.
result Every doubly semi-equivelar map on the torus contains a Hamiltonian cycle.
The study classifies semi-equivelar maps on Klein bottle.
problem Classifying semi-equivelar maps on Klein bottle.
method Enumerating and classifying a specific class of maps.
result Eleven types of semi-equivelar maps on Klein bottle are identified.
Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. In earlier work a complete classification of semi-equivelar map of type (35,4) on the surface of Euler characteristic -1 was given. In the meantime Karabas an Nedela classified vertex transitive semi-equivelar maps on…
Study of maps with -2 Euler characteristic and up to 12 vertices.
problem Enumerating and classifying semi-equivelar maps with specific Euler characteristics.
method Comprehensive enumeration and classification of semi-equivelar maps on a surface with χ=-2, up to 12 vertices.
result Determination of maps' vertex-transitivity and non-transitivity.
The article explores symmetric maps on surfaces, focusing on semi-equivelar maps.
problem Identifying and classifying semi-equivelar maps on surfaces with specific Euler characteristics.
method Analyzing automorphisms and symmetry groups of maps on higher genus surfaces.
result There are at least 39 types of semi-equivelar maps on surfaces with Euler characteristic -2m, m ≥ 2, with symmetry groups isomorphic to dihedral or cyclic groups.
Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types {33,42}, {32,4,3,4}, {6,3,6,3}, {34,6}, {4,82}, {3,122}, {4,6,12}, {6,4,3,4} exist on the torus. In this article we show the e…
We present enumerations of a class of toroidal graphs which give rise to semi-equivelar maps. There are eleven different types of semi-equivelar maps on the torus. These are of the types {36}, {44}, {63}, {33,42}, {32,4,3,4}, {3,6,3,6}, {34,6}, {4,82}, $\…
Classifies semi-equivelar gems on surfaces with Euler characteristic -1.
problem Classifying semi-equivelar gems on surfaces with negative Euler characteristic.
method Regular colored graphs representing PL d-manifolds, cyclic sequence of face degrees around vertices. result Identifies 12 types of semi-equivelar gems for surfaces with Euler characteristic -1.
This paper classifies semi-equivelar gems on a double torus.
problem Classifying semi-equivelar gems on surfaces with negative Euler characteristic.
method Regular colored graphs representing the double torus, with identical cyclic face degree sequences around each vertex.
result 31 types of semi-equivelar gems on the double torus.
The article explores the mapping class group using unicellular maps and provides filtrations.
problem Understanding the structure of the mapping class group.
method Using unicellular maps and surgeries, the article describes the mapping class group.
result Provides filtrations of the mapping class group.
Constructs a moment map flow for isotropic maps on surfaces.
problem Understanding isotropic maps on surfaces and their properties.
method Develops a Kähler moment map geometry and a modified moment map flow.
result Polyhedral modified moment map flow induces a strong deformation retraction.
Deep learning classifies seven types of maps for better access.
problem Efficiently accessing the right map type from digital maps.
method Used deep convolutional neural networks to classify seven types of maps.
result Deep learning can accurately classify different types of maps.
The paper constructs biharmonic maps between spheres using polynomial maps.
problem Creating biharmonic maps between spheres.
method Using harmonic homogeneous polynomial maps of different degrees to generate proper biharmonic maps.
result Established a method for constructing proper biharmonic product maps.
Both bi-harmonic map and f-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study f-bi-harmonic maps as the critical points of the f-bi-energy functional 21∫Mf∣τ(φ)∣2dvg. This class of maps generalizes both …
Generic pseudo-Anosov mapping classes in mapping class groups.
problem Understanding the prevalence of pseudo-Anosov mapping classes.
method Proving genericity with respect to specific notions of genericity.
result Pseudo-Anosov mapping classes are generic in mapping class groups.
Paper constructs maps for sutured monopole Floer homology.
problem None explicitly stated in the abstract.
method Constructs gluing and cobordism maps for sutured monopole Floer homology.
result Developed mathematical tools for sutured monopole Floer homology.
The paper generalizes Reeb spaces for special generic maps and lifts smooth functions.
problem Constructing lifts of smooth maps, especially Morse functions.
method Defining and generalizing quotient maps onto Reeb spaces of special generic maps and constructing lifts.
result Lifts of Morse functions can be constructed using the generalized maps.
Research explores real algebraic realization of round fold maps of codimension -1.
problem Real algebraic realization of round fold maps of codimension -1.
method Generalizes canonical projections of unit spheres to round fold maps and discusses their real algebraic realization.
result Developed new studies in real algebraic geometry focusing on round fold maps of codimension -1.
Study shows pure mapping classes can generate pseudo-Anosov mapping classes with certain conditions.
problem Understanding when pure mapping classes generate pseudo-Anosov mapping classes.
method Analyzing products of a given mapping class and powers of pure mapping classes, deriving an explicit constant.
result Almost all pure mapping classes generate pseudo-Anosov mapping classes when their powers exceed a certain constant.
The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.
problem Deriving Liouville theorems for generalized maps on Riemannian manifolds.
method Using conservation laws and monotonicity formulas, the paper derives Liouville theorems for different types of maps under various conditions.
result The paper establishes Liouville theorems for several types of generalized maps, including φ-F harmonic maps, φ-F symphonic maps, and φ-F-V-harmonic maps. Study of liftable mapping class group for superelliptic covers.
problem Understanding mapping class groups of superelliptic covers.
method Computational and algebraic methods to study the liftable mapping class group.
result The liftable mapping class group is independent of the degree of the cover and has finite abelianization.
Paper defines and studies Clairaut warped product Riemannian maps.
problem Understanding the geometry of specific Riemannian maps.
method Identify geodesic conditions, derive conditions for Clairaut maps, and calculate curvature.
result Found conditions for a warped product Riemannian map to be Clairaut.
Study shows no boundary maps for certain groups.
problem Existence of boundary maps for hierarchically hyperbolic spaces.
method Analysis of right-angled Artin groups and mapping class groups.
result Negative results on boundary maps for some groups.
The paper explores unique continuation properties for polyharmonic maps between Riemannian manifolds.
problem Investigating unique continuation principles for polyharmonic maps.
method Analyzing critical points of higher order functionals to prove extensions of known results in harmonic and biharmonic cases.
result Proving extensions of unique continuation principles for k-harmonic maps.
This paper constructs real algebraic maps that are topologically special generic maps.
problem Constructing smooth maps in differential topology and real algebraic geometry.
method Constructs real algebraic maps that are topologically special generic maps.
result Real algebraic maps are topologically special generic maps.
Derives stress-energy tensor for polyharmonic maps.
problem Characterizing polyharmonic maps between Riemannian manifolds.
method Derives stress-energy tensor and uses it to characterize polyharmonic maps.
result Characterizes polyharmonic maps, focusing on triharmonic maps.
The paper constructs gluing maps for harmonic maps between Riemannian manifolds.
problem Constructing harmonic maps between Riemannian manifolds.
method Gluing construction of extended harmonic maps.
result Construction of gluing maps for harmonic maps under specific conditions.
Characterizes a general range decreasing group homomorphism.
problem Understanding range decreasing group homomorphisms in the entire mapping group.
method Characterization of a general range decreasing group homomorphism.
result Computes a particular class of homomorphisms and identifies all range decreasing group homomorphisms on specific mapping groups.
The paper examines HM-tensional and HS-tensional maps between Riemannian manifolds.
problem Analyzing tension fields of maps between Riemannian manifolds.
method Investigating harmonic maps and harmonic sections as tension fields.
result Characterization and properties of HM-tensional and HS-tensional maps. The paper proves a Liouville theorem for specific harmonic maps with free boundary.
problem Analyzing harmonic maps with free boundary conditions.
method Developed Liouville theorem for φ-F-symphonic, φ-F-harmonic, and φ-ΦS,p,ε harmonic maps. result Established Liouville theorem for the specified harmonic maps with free boundary.
Dirac-harmonic maps are uncoupled under certain conditions.
problem Understanding the uncoupling of Dirac-harmonic maps.
method Critical points of a super-symmetric energy functional, with focus on harmonic maps.
result Dirac-harmonic maps are uncoupled under minimality assumption.
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.
We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficie…
The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.
problem Analyzing maps between pseudo-Hermitian and Kähler manifolds.
method Investigates partial energy functionals and critical maps, proving foliated results for ∂b- and ∂b-harmonic maps. result Generalizes Siu's holomorphicity result to ∂b- and ∂b-harmonic maps. The article explores constructing biharmonic and conformal biharmonic maps to spheres.
problem Constructing biharmonic and conformal biharmonic maps to spheres.
method Geometric algorithm to render harmonic maps biharmonic or conformally biharmonic.
result Explicit critical points for conformal-biharmonic maps between spheres are found.
Analyzes harmonic and biharmonic maps from gradient Ricci solitons.
problem Characterizing maps from gradient Ricci solitons.
method Derives conditions for maps to be constant or harmonic.
result Biharmonic maps of finite energy from the two-dimensional cigar soliton are harmonic.
Characterizes conformal Gauss maps into spheres.
problem Understanding conformal Gauss maps of surfaces.
method Invariant formulation and proof of characterisation of harmonic maps.
result Characterisation of harmonic maps as conformal Gauss maps of Willmore surfaces.
New theorem proves convergence of various discrete conformal structures to conformal maps.
problem Proving convergence of discrete conformal structures to conformal maps.
method General theorem using piecewise linear discrete conformal mappings and Riemannian barycentric coordinates.
result Discrete conformal mappings converge to conformal maps under certain conditions.
Method computes harmonic and conformal maps from point clouds.
problem Computing maps from irregular point cloud data.
method Meshless method using cubic lattice approximations.
result Harmonic and conformal maps computed accurately.
In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic maps. Moreover, we investigate the relation among CMC-surfaces by use of such maps.
Harmonic map flow preserves almost-holomorphic maps without singularities.
problem Preserving almost-holomorphic maps without singularities.
method Harmonic map flow applied to almost-holomorphic maps.
result No singularities or necks appear in the limit at singular times.