Study periodic geodesics on contact 3D manifolds, proving existence and precise properties.
problem Existence and properties of periodic geodesics in contact sub-Riemannian metrics.
method Develops two independent subjects: existence of spiraling geodesics and precise study of geodesics on quotient of SL2(R).
result Proves existence and precise properties of periodic geodesics.
3D metrics get scalar curvature bounds via IMCF.
problem Bounding scalar curvature for C0 metrics. method Inverse Mean Curvature Flow (IMCF) and Hawking mass monotonicity.
result Stability theorem for nonnegative scalar curvature.
Study finds symmetries in a special 3D space with a diagonal metric.
problem Identifying symmetries in a specific 3D space.
method Determining Killing vector fields on a diagonal metric in R3. result Killing vector fields on the space R3 with a diagonal metric have been identified. Detect spacetime curvature without rulers and clocks in 3D.
problem Detecting spacetime curvature without traditional measurement tools.
method Generalized results from 2D to 3D spacetime, proving well-stitched spacetime for conformally flat cases.
result A 3D spacetime is well-stitched if and only if it is conformally flat, providing a tool for curvature detection.
3D spherical caps are rigid under certain perturbations.
problem Rigidity of 3D spherical caps under specific perturbations.
method Gromov's μ-bubble technique
result 3D spherical caps are rigid under perturbations that maintain metric, scalar curvature, and mean curvature.
Solves Besse conjecture on 3D manifolds, proving metric rigidity.
problem Besse conjecture on 3D compact manifolds
method Analytical proof of critical point equation
result Proves rigidity of Miao-Tam metric
Paper develops a new method to analyze 3D tree-like objects.
problem Analyzing complex geometrical and topological variations in 3D tree-like objects.
method Extended SRVF representation and new metric for tree-shaped 3D objects.
result Captures full elasticity and topological variations of branches.
Proves existence of at least two minimal spheres in any 3D space.
problem Existence of minimal spheres in arbitrary 3D spaces.
method Iterative relative min-max constructions.
result Proves existence of at least two embedded minimal spheres.
The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is examined in the light of the role played by topological three dimensional (3D) Taub-N…
Study on flat metrics on 3D and 4D manifolds, focusing on topology and algebra.
problem Topology and algebraic structure of flat metrics on manifolds.
method Algebraic and topological descriptions of moduli spaces.
result Algebraic description and topology of moduli spaces for 4D manifolds with a single holonomy generator.
Establishes smooth Ricci flows from convex surfaces in 3D space.
problem Existence and uniqueness of Ricci flow starting from convex surfaces.
method Smooth Ricci flows starting from smooth convex surfaces.
result Uniform convergence of metrics to initial convex surface.
3D models vulnerable to adversarial attacks, new method improves success rate and naturalness.
problem Vulnerability of 3D deep learning models to adversarial examples in the physical world.
method ε-isometric (ε-ISO) attack considering geometric properties and invariance to physical transformations. result Significantly improved attack success rate and naturalness of 3D adversarial examples.
The two-loop renormalization group flow is studied via the induced bracket flow on 3D unimodular Lie groups. A number of steady solitons are found. Some of these steady solitons come from maximally symmetric metrics that are steady, shrinking, or expanding solitons under Ricci flow, while others are not obviously relat…
Study of symmetries in 3D Lie groups, determining index and moduli space properties.
problem Understanding symmetries in 3D Lie groups and their moduli space.
method Computed full isometry groups of left-invariant metrics on 3D Lie groups.
result Determined index of symmetry and properties of moduli space.
Study 3D manifolds with specific curvature conditions.
problem Characterize 3D generalized (κ,μ)-contact metric manifolds. method Analyze manifolds with ildeW⋅R=0 and ildeW⋅H=0. result Cover all eight equivalent classes of 3D manifolds.
The paper classifies 3D paracontact and almost paracosymplectic spaces.
problem Classifying 3D paracontact and almost paracosymplectic spaces.
method Detailed structure analysis and local classification for all possible values of κ.
result Local classification of paracontact metric and almost paracosymplectic (κ,μ)-spaces for every possible value of κ.
The study classifies minimal translation surfaces in 3D and 3D_1.
problem Classifying minimal translation surfaces in specific geometric settings.
method Defined and classified minimal translation surfaces with semi-symmetric connections.
result New classification of minimal translation surfaces in R3 and R13. The paper proves conjectures and classifies metrics on 3D manifolds.
problem Proving conjectures and classifying metrics on 3D manifolds with specific curvature conditions.
method Analytical proofs and classification theorems.
result Critical metrics on 3D manifolds are isometric to geodesic balls in space forms.
3D object detection improved using energy-based models.
problem Accurate 3D object detection in cluttered environments from sparse LiDAR data.
method Designing a differentiable pooling operator for 3D bounding boxes integrated into a state-of-the-art 3D object detector.
result Our approach consistently outperforms the SA-SSD baseline across all 3DOD metrics on the KITTI dataset.
The Fefferman metric connects CR manifolds to conformal geodesics in 3D.
problem Understanding the Fefferman metric on CR manifolds.
method Explicit description of the Fefferman metric and variational characterization of conformal geodesics.
result Conformal geodesics have lifts to chains and null chains, and are characterized by total torsion.
Paper shows non-CSC HCMU metrics can't be isometrically immersed into 3D space forms.
problem Non-CSC HCMU metrics cannot be isometrically immersed into 3D space forms.
method Using moving frames to demonstrate the impossibility of isometric minimal immersion.
result Non-CSC HCMU metrics cannot be isometrically immersed into 3D space forms.
3D Axial-Attention improves lung nodule classification accuracy.
problem Limited 3D attention in existing methods.
method Proposes 3D Axial-Attention network with 3D positional encoding.
result 3D Axial-Attention achieves state-of-the-art performance.
Study on 3D Lie groups finds all generalized Einstein metrics.
problem Classifying generalized Einstein metrics on 3D Lie groups.
method Developed theory of left-invariant generalized pseudo-Riemannian metrics, computed Ricci tensor, determined all metrics.
result Determined all generalized Einstein metrics on three-dimensional Lie groups.
Study odd generalized Einstein metrics on 3D Lie groups.
problem Classify odd generalized Einstein metrics on 3D Lie groups.
method Left-invariant generalized connections, divergence operators, and Ricci tensors.
result Describe all odd generalized Einstein metrics on all 3D Lie groups.
The only known example of collapsed three-dimensional complete gradient steady Ricci solitons so far is the 3D cigar soliton N2×R, the product of Hamilton's cigar soliton N2 and the real line R with the product metric. R. Hamilton has conjectured that there should exist a family of colla…
Diagonalizes metrics of 3D Lorentzian manifolds.
problem Diagonalizing metrics of 3D Lorentzian manifolds.
method Applying the technique of moving frames.
result Every smooth Lorentzian 3-manifold admits an atlas with a diagonal metric.
Complete Calabi-Yau metrics made on special 3D spaces.
problem Creating complete Calabi-Yau metrics on complex 3D spaces.
method Used gluing construction and perturbation argument.
result Produced complete Calabi-Yau metrics with unbounded curvature.
We present a method of generating high resolution 3D shapes from natural language descriptions. To achieve this goal, we propose two steps that generating low resolution shapes which roughly reflect texts and generating high resolution shapes which reflect the detail of texts. In a previous paper, the authors have show…
We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riema…
The polynomial affine model of gravity is explored in 3D, focusing on cosmological solutions.
problem Exploring deviations from general relativity in a 3D context.
method Developed a polynomial affine model of gravity, applied to homogeneous isotropic cosmological models, and classified solutions.
result Explicit solutions derived from the connection allow the definition of alternative/emergent metrics.
PolyGen models 3D meshes directly, predicting vertices and faces sequentially.
problem Efficiently modeling 3D geometry for computer graphics, robotics, and games.
method Transformer-based autoregressive model for predicting mesh vertices and faces.
result PolyGen produces high-quality, usable 3D meshes and competitive conditional performance.
New techniques solve Riccati equations on 3D manifolds, finding 4th order metric obstructions.
problem Solving Riccati-type equations with algebraic constraints on 3D Riemannian manifolds.
method Real algebraic geometry techniques, focusing on connection coefficients and Hessian equations.
result Obstruction to solving Riccati equations has order 4 in metric coefficients.
A 3D almost-Riemannian manifold is a generalized Riemannian manifold defined locally by 3 vector fields that play the role of an orthonormal frame, but could become collinear on some set $\Zz$ called the singular set. Under the Hormander condition, a 3D almost-Riemannian structure still has a metric space structure, wh…
The paper constructs and classifies 3D Walker manifolds with specific structures.
problem Classifying 3D Walker manifolds with specific paracontact structures.
method Constructing structures using a unit space-like vector field and a function, characterizing the Lorentzian metric.
result Necessary and sufficient conditions for the manifold to belong to specific classes of almost paracontact metric manifolds.
The paper studies rigid sphere packings on 3D manifolds with boundary.
problem Investigating rigid sphere packings on 3D manifolds with boundary.
method Introducing generalized sphere packings, proving rigidity, introducing combinatorial curvature flows.
result Generalized sphere packing metrics are determined by combinatorial scalar curvature.
Study of null φ-slant curves in specific 3D manifolds.
problem Characterizing null φ-slant curves in 3D normal almost contact B-metric manifolds.
method Analyzing the geometric properties and Frenet frames of φ-slant null curves.
result Existence of a unique Frenet frame for non-geodesic φ-slant null curves.
Study on 3D manifolds with circulant structures and their properties.
problem Characterizing 3D almost Einstein manifolds with circulant structures.
method Analyzing the curvature tensor and properties of the Levi-Civita connection.
result Determined geometric characteristics and examples of such manifolds.
The sigma invariant is studied for torus, K3 surface, and 3d manifolds.
problem Investigating the sigma invariant for specific manifolds.
method Analyzing isometric embeddings and scalar curvature functionals.
result Sigma invariant is zero for torus, K3 surface, and certain 3d manifolds.
Study finds metrics maximizing one Laplace eigenvalue on 3D and higher manifolds.
problem Maximizing a Laplace eigenvalue on n-dimensional manifolds.
method Existence and regularity results for metrics of same volume in a conformal class.
result Existence and regularity of metrics maximizing the Laplace eigenvalue.
New framework segments 3D scenes using neural algorithms and sub-Riemannian geometry.
problem Effective scene segmentation in 3D vision.
method Neurogeometric sub-Riemannian model, harmonic analysis, neural-based stereo correspondence.
result Sub-Riemannian metric is central to effective scene segmentation.
Study investigates induced geometry on surfaces in 3D contact manifolds.
problem Understanding the metric structure on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Defined a coefficient to characterize characteristic points and identified global conditions for finite induced distance.
result Proved induced distance finite for certain surfaces with isolated characteristic points.
Improves AI agents' 3D navigation by learning from failures and 3D spatial relationships.
problem Challenges in data efficiency, obstacle avoidance, and generalization in 3D visual navigation.
method Incorporates attention on 3D spatial relationships and a target skill extension module into DRL framework.
result Significantly improves navigation performance and generalization across targets and scenes.
SCENE-Net improves 3D point cloud segmentation with low resource usage and transparency.
problem Lack of resources and transparency in 3D semantic segmentation models.
method SCENE-Net uses signature shapes identified via GENEOs to achieve semantic segmentation with minimal resources.
result SCENE-Net achieves comparable IoU to state-of-the-art methods with less data and computational resources.
New metrics solve complex equations on special 3D shapes.
problem Finding metrics on complex 3D shapes.
method Gluing construction to solve equations.
result Solves dilatino equation on small resolutions.
Develops Llarull type theorems for 3D and 4D bands with spectral scalar curvature bounds.
problem Bounding scalar curvature and metric on 3D and 4D bands simultaneously.
method Warped μ-bubble method result Establishes Llarull type theorems for 3D and 4D bands with spectral scalar curvature bounds.
Paper proves rigidity of metrics near hyperbolic ones in 3D.
problem Proving rigidity of metrics near hyperbolic ones in 3D.
method Introducing marked Poincaré determinant and proving local rigidity.
result Lichnerowicz Laplacian is injective in negative curvature.
This work generates synthetic 3D thermal facial data using 2D facial data and deep learning.
problem Creating large datasets for deep learning in computer vision.
method 3D facial modelling techniques and deep learning methodologies.
result Synthetic 3D thermal facial data created for deep learning applications.
Study classifies special metrics for which the isometry group of 3D Lie groups is larger than expected.
problem Classifying metrics for which the isometry group of 3D Lie groups is larger than expected.
method Lie-theoretical methods to classify pairs (G, g)
result Determines the dimension of the isometry group for every pair (G, g)