Synthetic construction of Hopf fibration in 4D space.
problem Visualizing 4D objects in 3D space.
method Double orthogonal projection method to visualize 4D space.
result Direct synthetic construction of 3-sphere fibers from 2-sphere points.
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48 results for “4D visualization”
Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient processing and interpretation of large volumes of data remain challenging, especi…
Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.
problem Understanding the relationship between 4d and 3d BPS quivers.
method Analyzes geometric backgrounds and uses skein modules to derive quiver partition functions.
result Proves isomorphism between 4d wall-crossing and unlinking of symmetric quivers.
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…
New 1-parameter family of ovals identified in 4d Ricci flow classification.
problem Classifying -solutions in 4d Ricci flow.
method Introducing conjectures and constructing new examples.
result Established canonical neighborhood theorem for 4d Ricci flow.
Study of 4D Ricci solitons with symmetry, finding precise geometric asymptotics.
problem Classifying 4D gradient steady Ricci solitons and understanding their geometric properties.
method Analysis of 4D gradient steady Ricci solitons with O(3)-symmetry under a weak curvature decay condition.
result Find precise geometric asymptotics similar to 3D compact κ-solutions.
Study 4D solitons with specific curvature properties, proving curvature bounds and classifying solutions.
problem Investigate 4D gradient solitons with specific curvature properties.
method Analyze 4D gradient steady and shrinking solitons with nonnegative or half nonnegative isotropic curvature.
result Prove 2-nonnegativity of Ricci curvature and bound the curvature tensor for ancient solutions.
New minimal surfaces in 4D space derived from parametric equations.
problem Deriving explicit parametric equations for higher-order Henneberg-type minimal surfaces in .
method Generalized Weierstrass--Enneper representation and differential geometric analysis.
result Explicit parametric equations and differential geometric characteristics of the Henneberg-type minimal surfaces in .
Study classifies special 4D shapes with certain curvature.
problem Classifying specific types of 4D shapes.
method Classifying compact almost-Kähler four manifolds with nonnegative biorthogonal curvature.
result Classified compact almost-Kähler four manifolds with nonnegative biorthogonal curvature.
Perelman's proof confirmed, new method uses 4D topology.
problem Confirming the classical Poincaré conjecture.
method 4D topology, spun torus-knots, ribbonness, disk-chord system, Bing's result.
result Homotopy 3-sphere is diffeomorphic to the 3-sphere.
A class of 3d supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction in 3d/3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class…
Nearly Kaehler Reductionhep-th
We consider compactification of type IIA supergravity on nearly Kaehler manifolds. These represent a simple class of SU(3) structure manifolds which includes S^6 and CP^3. We exhibit for the first time an explicit reduction ansatz in this context, obtaining an N=2 gauged supergravity in 4d with a single vector and hype…
Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theoryhep-th
We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at (SU(2) YM), by turning on backg…
New surfaces generalize Dini surfaces in 4D.
problem None explicitly stated; focuses on surface generalization.
method Introducing a new family of surfaces in 4D.
result Generalized Dini surfaces exist in 4D.
Corks and exotic ribbons in math.GT
New ribbon disks in 4D space, non-isotopic to each other.
problem Non-isotopic ribbon disks in 4D.
method Using corks to construct diffeomorphic ribbon disks.
result Non-isotopic ribbon disks constructed in 4D.
The study calculates harmonic functions and 1-forms on specific 4D spaces.
problem Computing harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds.
method Computed the expansion of harmonic functions and 1-forms.
result Computed the expansion of harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds.
Study of symmetries in 4D Lie groups.
problem Understanding symmetries in specific Lie groups.
method Analyzing isometry groups of left-invariant metrics.
result Full description of isometry groups for 4D Lie groups.
Simultaneous Monitoring of Shape and Surface Color via 4D Point Clouds: A Registration-free Approachcs.CV
A registration-free framework monitors shape and color in 4D point clouds.
problem Monitoring shape and color changes in complex parts without registration.
method Laplace-Beltrami operator spectral properties for geometric and color feature capture; combined monitoring scheme for shape and color anomalies.
result Effective detection of shape deformations and color anomalies without registration or mesh reconstruction.
Minimal moves for surfaces in 4D identified.
problem Classifying surfaces embedded in 4D space.
method Derived minimal generating set of planar moves.
result Identified minimal moves for surfaces in 4D.
Method resolves 4D symplectic orbifolds using complex geometry.
problem Resolving symplectic orbifolds in 4 dimensions.
method Combining complex geometry techniques with symplectic form gluing.
result Examples of 4D symplectic orbifolds successfully resolved.
Study describes flat metric moduli spaces on 4D manifolds.
problem Understanding flat metrics on 4D closed manifolds.
method Algebraic and topological description of moduli spaces.
result Algebraic and topological description of moduli spaces of flat metrics.
The paper classifies singularities of line congruences in 4D space.
problem Classifying singularities of line congruences in 4D space.
method Generic classification approach for 3-parameter line congruences and Blaschke normal congruences.
result Generic classification of singularities of 3-parameter line congruences in .
We study second-order PDEs in 4D for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solution. We prove that this requirement implies the Monge-Ampere property. Since half-flatness of the conformal structure is equivalent to the exi…
We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-parakaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures in dimension four.
Low entropy hypersurfaces in 4D are isotopic to a sphere.
problem Characterizing hypersurfaces with low entropy in 4D.
method Proving isotopy to the standard 3-sphere for hypersurfaces with entropy ≤ cylinder entropy.
result Closed hypersurfaces with low entropy are isotopic to the standard 3-sphere.
Sharp inequality proven for symmetric functions on a 4D sphere.
problem Proving a sharp Beckner's inequality for axially symmetric functions on .
method Utilized pointwise properties of Gegenbauer polynomials.
result Sharp Beckner's inequality established for axially symmetric functions on .
M-theory compactified on -holonomy manifolds results in 4d supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle…
The study examines 4D steady gradient Ricci solitons with nonnegative curvature away from a compact set.
problem Analyzing noncompact steady gradient Ricci solitons with nonnegative curvature operator.
method Examining the asymptotic behavior of noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative curvature operator away from a compact set.
result 4D noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature must be a Bryant Ricci soliton up to scaling.
Study uses superalgebra homology to classify 4D Engel-like Lie algebras.
problem Classifying 4-dimensional Engel-like Lie algebras.
method Applied homology groups of Lie superalgebras.
result Distinguished and classified 4D Engel-like Lie algebras.
The study examines Lipschitz normally embedded Hölder triangles in 4D space.
problem Comparing ambient and outer Lipschitz geometry of Hölder triangles.
method Analyzes Lipschitz normally embedded Hölder triangles in \(\mathbb{R}^4\).
result Infinitely many equivalence classes of microknots.
New theorem for 4D links simplifies characterisation problem.
problem Long-standing open problem in link characterisation.
method Reidemeister Theorem for solid ribbon torus links.
result Complete characterisation of a related class of links.
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems which state the conditions when two types of ansatz result in integrable gravitati…
Extends spectral Einstein functionals computation to 4D spin manifolds with boundary.
problem Computing spectral Einstein functionals for 4D spin manifolds with boundary.
method Generalizes Dabrowski's results to 4D spin manifolds with boundary using noncommutative residue.
result Generalized spectral Einstein functionals computation for 4D spin manifolds with boundary.
Global regularity proved for 4D Ricci flow with scalar curvature integral bound.
problem Global regularity of 4D Ricci flow with integral scalar curvature bound.
method Extended Ge-Jiang's result to include integral bound on scalar curvature.
result Global -regularity for 4D Ricci flow with integral scalar curvature bound.
New deep learning method improves 4D Flow MRI super-resolution under domain shift.
problem Domain shift in low-resolution 4D Flow MRI data.
method Distributional deep learning framework for domain generalization.
result Framework significantly outperforms traditional methods in real data applications.
New infinite family of 2-complexes intrinsically linked in 4D.
problem Intrinsic linking of 2-complexes in 4D.
method Examining suspensions of graphs containing K6 as a minor.
result Embeddings of suspensions contain intrinsically linked cycles.
Minimal hypertori found in 4D sphere, solving Bernstein conjecture.
problem Finding minimal embedded hypertori in 4D sphere.
method Analyzing minimally embedded and immersed hypertori and hyperspheres.
result Infinitely many non-isometric minimally embedded hypertori and hyperspheres found.
We show how wall-crossing formulas in coupled 2d-4d systems, introduced by Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the deformation theory of holomorphic pairs, given by a complex manifold together with a holomorphic vector bundle. The main part of the paper studies the relation between …
Scroll structures on solutions of 4D integrable equations are involutive and governed by a dispersionless hierarchy.
problem Characterizing the geometry of solutions to 4D integrable equations.
method Defining rational normal scrolls and showing their involutivity.
result Involutive scroll structures are governed by a dispersionless integrable hierarchy.
Minimal surfaces found in 4D space.
problem Minimal surfaces in 4D space.
method Reduced biharmonic equation to ODEs, excluded non-minimal solutions.
result Biharmonic rotational surfaces in 4D are minimal.
Novel singularity models for 4D harmonic forms and spinors from polytopes.
problem Understanding harmonic forms and spinors in 4D.
method Homogeneous singularity models based on regular 4-polytopes.
result Models describe cones on the 1-skeletal of polytopes.
Paper proves rigidity of certain 2D Lagrangian shapes in 4D space.
problem Proving rigidity of specific Lagrangian shapes in 4D space.
method Used a rigidity theorem for 2D complete Lagrangian self-shrinkers.
result Rigidity of 2D complete Lagrangian self-shrinkers with constant squared norm of mean curvature vector.
We study integrable non-degenerate Monge-Ampere equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining the equations. This is used to deform these heavenly type equations into new integrable PDE of the second order with large symmetry pseu…
In arXiv:1005.3255 we proved an orbifold Cheeger-Gromov compactness theorem for complete 4d Ricci shrinkers with a lower bound for the entropy, an upper bound for the Euler characterisic, and a lower bound for the gradient of the potential at large distances. In this note, we show that the last two assumptions in fact …
Deep Learning Framework for History Matching CO2 Storage with 4D Seismic and Monitoring Well Datacs.LG
Deep learning calibrates CO2 storage formations from seismic and well data.
problem Uncertainty in CO2 storage formation properties.
method Two deep learning models for well and seismic data, integrated into MCMC history matching.
result Significant uncertainty reduction in key parameters and accurate CO2 plume predictions.
Integrability of dispersionless Hirota type equations in 4D and the symplectic Monge-Ampere propertynlin.SI
We prove that integrability of a dispersionless Hirota type equation implies the symplectic Monge-Ampere property in any dimension . In 4D this yields a complete classification of integrable dispersionless PDEs of Hirota type through a list of heavenly type equations arising in self-dual gravity. As a by-produc…
Algorithm constructs Kirby diagrams for 4D open books.
problem Constructing Kirby diagrams for 4D open books.
method Algorithm using Heegaard diagrams of pages.
result Diffeomorphic open books constructed with different pages and monodromies.
For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the sense of Agrachev-Zelenko-Li. Under appropriate bounds we prove comparison theorems for conjugate lengths, Bonnet-Myers type results and Laplacian comparison theorems for the intrinsic sub-Laplacian. As an application, we consider …