Positive factorization found for a specific map on surfaces.
problem Balanced superelliptic rotation on surfaces.
method Positive factorization approach.
result Positive factorization for balanced superelliptic rotation.
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48 results for “rotation map”
In this paper we study general rotational surfaces in the 4- dimensional Euclidean space E4 and give a characterization of flat general rotation surface with pointwise 1-type Gauss map. Also, we show that a non-planar flat general rotation surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Cl…
In this paper, we study rotational surfaces of elliptic, hyperbolic and parabolic type with pointwise 1-type Gauss map which have spacelike profile curve in four dimensional pseudo Euclidean space E4-2 and obtain some characterizations for these rotational surfaces to have pointwise 1-type Gauss map.
In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space E4-2 and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in E4-2 and give an example of such surfaces.
Study on unfolding maps of surfaces in 3D space, proving versality conditions.
problem Investigating the versality of rotation unfolding of folding maps for surfaces in .
method Introducing and analyzing the rotation unfolding of folding maps, proving versality conditions in terms of geometry.
result Proved conditions for the rotation unfolding to be versal, showing diffeomorphic type of tangent plane locus.
Study of calorons with rotation map symmetry.
problem Understanding the symmetry groups of calorons.
method Utilizing a modified ADHM construction for calorons, derived from Charbonneau and Hurtubise's work.
result Construction of new calorons through fixed points of symmetry groups.
Rotates MFVI for better Gaussian approximations.
problem Improving variational approximations for complex distributions.
method Rotated coordinate system, PCA-based rotation, iterative Gaussianization.
result Significantly more accurate approximations with lower computational cost.
In-plane drill rotations are impossible for smooth shells.
problem In-plane drill rotations on smooth shells are impossible.
method Analyzing the differential geometry of surfaces and isometries.
result Any isometry that coincides with the given surface at a portion of the boundary is the identity.
In this work, we study some classes of rotational surfaces in the pseudo-Euclidean space with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space with pointwise 1-type Gauss map of the first kind and second kind. Then, we obtain …
A method improves Cryo-EM 3D map refinement by regularizing rotation estimation.
problem Noise-robustness vs. data-consistency in Cryo-EM 3D map reconstruction.
method Ellipsoidal support lifting (ESL) for regularizing and approximating the global minimizer over Riemannian manifolds.
result The induced bias due to regularizing effect of ESL estimates better rotations than global optimisation.
Harmonic Networks make images equivariant to translation and rotation.
problem Making CNNs equivariant to rotation.
method Replacing CNN filters with circular harmonics to achieve patch-wise translation and 360-degree rotation equivariance.
result Deep feature maps encode complicated rotational invariants.
Study shows only rotations can be approximated by Ginzburg-Landau critical points.
problem Proving not all harmonic maps can be approximated by Ginzburg-Landau critical points.
method Rigidity theorem applied to Ginzburg-Landau energy critical points.
result Only rotations can be approximated by Ginzburg-Landau critical points.
The rotation angle of a rolling disc is shown to be a geometric phase related to the Hopf fibration.
problem Understanding the geometric nature of rotation angles in kinematic models.
method Using the Hopf fibration and Gauss map, the geometric phase is decomposed into dynamical and geometric components.
result The geometric phase of rotation is described as the holonomy of the Hopf fibration.
In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space E41. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface…
Improved sample efficiency in semantic segmentation with rotation equivariant CNNs.
problem Efficiently segmenting images with rotation and reflection symmetries.
method Introduced rotation-equivariant CNNs with new equivariant convolutions and transposed convolutions.
result Significant gains in sample efficiency and robustness to symmetry transformations.
The paper classifies rotational hypersurfaces in n-space using a modified Laplacian operator.
problem Classifying rotational hypersurfaces in n-dimensional Euclidean space.
method Investigating the Gauss map of rotational hypersurfaces with respect to the operator .
result Established a classification theorem connecting the matrix and the Gauss map through the equation .
We study the ergodic properties of compositions of interval exchange transformations and rotations. We show that for any interval exchange transformation T, there is a full measure set of αin [0, 1) so that T composed with R_α is uniquely ergodic, where R_α is rotation by α.
Optimal transport aligns rotated linear regression models across domains.
problem Aligning rotated linear regression models across domains with differing statistical properties.
method Combines K-means clustering, OT, and SVD to estimate rotation angle and adapt regression model.
result Optimal transport map recovers underlying rotation in .
Compact metric f-K-contact manifolds constructed via specific transformations.
problem Constructing all metric f-K-contact manifolds.
method Iteration of constructions of mapping tori, rotations, and type II deformations.
result Compact metric f-K-contact manifolds are derived from compact K-contact manifolds.
Study rotational surfaces with prescribed Gauss curvature in 3D space.
problem Classify and analyze rotational surfaces with prescribed Gauss curvature.
method Phase plane analysis and mild assumptions on the prescribed function.
result Existence of singular radial solutions intersecting orthogonally the axis of rotation.
Paper learns to rotate filters for group convolutions.
problem Difficult to rotate 3x3 filters on pixel grids.
method Learn filter basis and rotation-invariant coefficients; switch basis for rotation.
result Produces feature maps insensitive to input rotations.
Study classifies rotational hypersurfaces with prescribed mean curvature.
problem Classifying rotational hypersurfaces with prescribed mean curvature.
method Phase space analysis to classify hypersurfaces.
result Delacunay-type classification for even prescribed functions.
The normal map of curves is analyzed as a vector field on a cylinder.
problem Understanding the geometric properties of normal maps and their vector field interpretation.
method Interpreting critical points geometrically, studying Poincaré index, projecting to sphere, and analyzing winding and rotation indices.
result Counting theorems regarding winding and rotation indices of curves and their evolutes are proven.
New geometric interpretation of a group class using circle action and rotation numbers.
problem Understanding a specific class in the mapping class group.
method Action of the punctured mapping class group on the circle and rotation numbers.
result Construction matches Furuta and Trapp's using winding numbers.
New tree structure for pseudo-Anosovs from interval maps.
problem Understanding pseudo-Anosovs from interval maps.
method Tree structure on pseudo-Anosovs using rational numbers.
result Deepened dictionary between invariants.
Researchers generalize Ribaucour-type surfaces with new mathematical representation.
problem Defining and characterizing new geometric surfaces.
method Developed a new mathematical representation for GRT-surfaces involving holomorphic functions and a real function.
result Explicit examples and classification of GRT-surfaces of rotation.
New coefficient detects irrational rotation behavior on infinite-type surfaces.
problem Detecting irrational rotation behavior on surfaces of infinite type.
method Introducing a new quasimorphism, the Dehn twist coefficient, and proving its properties.
result The Dehn twist coefficient can have image all of R for some infinite-type surfaces.
The study proves conditions for hyperbolic isometries on fine curve graphs of higher genus surfaces.
problem Conditions for hyperbolic isometries on fine curve graphs of higher genus surfaces.
method Proves equivalence of conditions involving isotopic maps, pseudo-Anosov maps, and ergodic rotation sets.
result Ergodic homological rotation sets have nonempty interior for certain isotopic maps.
Defines spherical type surfaces via support function and classifies them.
problem Characterizing surfaces via support function.
method Weierstrass type representation for SS-surfaces with prescribed Gauss map.
result Every compact and connected SS-surface is the sphere.
New kernel interprets 3D anisotropic data with rotations and improved predictions.
problem Capturing rotated anisotropy in 3D spatial fields.
method Introduces a Lie-algebraic kernel with three principal length-scales and an explicit rotation.
result Posterior recovers rotated anisotropy and improves prediction over axis-aligned kernels.
The paper proposes a method to learn 3D object pose manifolds using GANs and elasticae.
problem Learning image manifolds of 3D objects with limited data.
method Geom-SGAN and elasticae for geometry-preserving image interpolation.
result The method outperforms state-of-the-art GANs and VAEs in learning rotation paths.
The projection body operator Π, which associates with every convex body in Euclidean space Rn its projection body, is a continuous valuation, it is invariant under translations and equivariant under rotations. It is also well known that Π maps the set of polytopes in Rn into itself. We show that Π is the only non-trivi…
Optimal transport aligns source and target distributions for linear regression in 2D.
problem Domain adaptation for linear regression in 2D with limited target data.
method Combining K-means and optimal transport for estimating geometric transformations.
result Optimal transport recovers geometric transformations like rotations, translations, and homotheties.
New neural network learns relevant transformations in data, improving object recognition.
problem Current equivariant architectures consider all possible transformations, ignoring relevant ones.
method Co-attentive equivariant neural networks that focus on co-occurring transformations.
result Outperforms conventional equivariant networks on rotated MNIST and CIFAR-10.
Analyzes Schouten square on specific Lie algebra extensions, revealing geometric and algebraic properties.
problem Analyzing Schouten square on specific Lie algebra extensions.
method Analyzes Schouten square on specific Lie algebra extensions $\g=\fb\oplus V\oplus\fb^{*}$, focusing on $\Rone$ and $\Rplus$.
result Schouten square splits orthogonally into radial and angular components, with radial component factoring through a moment map.
Abstract: Generalizes supergravity c-map to quaternionic manifolds.
problem Construct quaternionic manifolds from hypercomplex manifolds.
method Construct conical hypercomplex manifolds and associate quaternionic manifolds.
result Quaternionic manifolds can be associated to special complex manifolds.
Application of a unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian three-spacemath.DG
Unified formula for surfaces in Euclidean or Lorentzian 3-space.
problem Describe surfaces in Euclidean or Lorentzian 3-space.
method Unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian 3-space.
result Unified single equation for Kenmotsu-type formulas in Euclidean and Lorentzian 3-space.
Study the geometry of twistor spaces with rotating circle action.
problem Holomorphic symplectic geometry of twistor spaces.
method Interpreting Hitchin's meromorphic connection and studying critical points of moment maps.
result Residue of Hitchin's meromorphic connection serves as a moment map for the circle action.
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spacesmath.GR
We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the later one provides a natural framework for developing a geometric version of small cancel…
Given a closed hyperbolic surface , let $\cQF$ denote the space of quasifuchsian hyperbolic metrics on and $\cGH_{-1}$ the space of maximal globally hyperbolic anti-de Sitter metrics on . We describe natural maps between (parts of) $\cQF$ and $\cGH_{-1}$, called "Wick rotations", defined in te…
Study classifies special surfaces in space with translational and rotational symmetries.
problem Classifying surfaces with specific symmetries and densities.
method Analyzes -translating solitons with invariant properties under translations and rotations.
result Classifies all -translating solitons with invariant surfaces.
Study homeomorphisms on fine curve graph of surfaces, revealing new types of dynamics.
problem Understanding dynamics of homeomorphisms on fine curve graphs of surfaces.
method Analyzing the action of homeomorphisms on the fine curve graph and relating to classical curve graphs.
result Homeomorphisms induce parabolic isometries, and all positive reals are realized as asymptotic translation lengths.
Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining additive maps of star bodies. These inequalities provide generalizations of resu…
In this paper we study geodesic mappings of -dimensional surfaces of revolution. From the general theory of geodesic mappings of equidistant spaces we specialize to surfaces of revolution and apply the obtained formulas to the case of rotational ellipsoids. We prove that such -dimensional ellipsoids admit non tri…
Limits of -harmonic mapsmath.DG
Critical points of approximations of the Dirichlet energy à la Sacks-Uhlenbeck are known to converge to harmonic maps in a suitable sense. However, we show that not every harmonic map can be approximated by critical points of such perturbed energies. Indeed, we prove that constant maps and the rotations of are th…
We prove that, in general, given a -harmonic map and a convex function , the composition is not -subharmonic. By assuming some rotational symmetry on manifolds and functions, we reduce the problem to an ordinary differential inequality. The key of the proof is an asymptotic…
Positive Dehn twist products for some elements of finite order in the mapping class group of a 2-dimensional closed, compact, oriented surface , which are rotations of through , are presented. The homeomorphism invariants of the resulting simply connected symplectic 4- manifolds are computed.
Study of two actions of mapping class groups on a graph and circle.
problem Understanding dynamics of mapping class groups on graphs and circles.
method Definition and proof of equators, hyperbolic graph, and circle embedding; construction of quasimorphisms.
result Loxodromic elements in the first action have rational rotation numbers in the second action.