The paper proposes methods for volumetric parameterization of 3D solid manifolds.
problem Complex structure of solid manifolds makes conventional approaches ineffective.
method Incorporates models to preserve geometric structure, achieve density equalization, and balance distortions.
result Various 3D manifold parameterizations with different properties can be achieved.
Defines a new 3D TQFT from non-semisimple categories.
problem Developing a TQFT from non-semisimple categories.
method Generators and relations framework, decomposition of 3-manifolds.
result TQFT values on 3-manifolds match known invariants.
This note generalizes the visual angle to convex sets in 3D space.
problem Analyzing geometric properties of convex sets in 3D space.
method Generalizing the visual angle to convex sets in Euclidean space and expressing geometric quantities in terms of integrals of functions related to the solid angle.
result Invariant quantities of the original convex set can be expressed by integrals of functions related to the solid angle.
Generative model calibrates 3D battery cathode morphologies from 2D images.
problem Calibrate 3D morphologies of all-solid-state battery cathodes from 2D microscopy images.
method Combining GANs with excursion sets of Gaussian random fields.
result Calibrated digital twins enable systematic exploration of morphological scenarios.
Modeling 3D continua with singular points using Yin sets.
problem Treat singular points as central subjects in 3D continuum topology.
method Model 3D continua as Yin sets, regular open semianalytic sets with bounded boundary.
result Characterize local and global topology of Yin sets.
Proves formula for 3D index change with Dehn filling.
problem Transforming 3D index under Dehn filling.
method Relative 3D index, gluing principle, inductive framework, q-hypergeometric functions.
result Rigorous proof of Gang-Yonekura formula.
Minimal surfaces span periodic curves in 3D space.
problem Existence of minimal surfaces spanning periodic curves.
method Proof of existence for minimal surfaces using periodic curves in R3. result Existence of noncompact simply connected periodic minimal surfaces.
We use the 3d-3d correspondence together with the DGG construction of theories Tn[M] labelled by 3-manifolds M to define a non-perturbative state-integral model for SL(n,C) Chern-Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k=1 state-integ…
Differentiable voxelization for 3D meshes with GPU acceleration.
problem Efficient and accurate voxelization of 3D meshes.
method Differentiable voxelization using winding number and solid angles, with GPU acceleration and neural network deformation.
result State-of-the-art performance in accuracy and efficiency on the ShapeNet dataset.
From a pseudo-triangulation with n tetrahedra T of an arbitrary closed orientable connected 3-manifold (for short, {\em a 3D-space}) M3, we present a gem J′, inducing $\IS^3$, with the following characteristics: (a) its number of vertices is O(n); (b) it has a set of p pairwise disjoint couples of vertices …
The need for advanced materials has led to the development of complex, multi-component alloys or solid-solution alloys. These materials have shown exceptional properties like strength, toughness, ductility, electrical and electronic properties. Current development of such material systems are hindered by expensive expe…
Large prospective epidemiological studies acquire cardiovascular magnetic resonance (CMR) images for pre-symptomatic populations and follow these over time. To support this approach, fully automatic large-scale 3D analysis is essential. In this work, we propose a novel deep neural network using both CMR images and pati…
3D RadViz improves 3D data visualization of multidimensional datasets.
problem Tackles the challenge of visualizing multidimensional datasets in 3D.
method Develops RadViz3D, a 3D radial visualization tool with uniform anchor points.
result Improves the display of multidimensional datasets, especially for uncorrelated variables.
Study on knots in contact manifolds, focusing on their width and thickness.
problem Understanding the width and thickness of knots in contact manifolds.
method Analyzing solid tori, defining width, and comparing it to Thurston-Bennequin invariant.
result Existence of non-thickenable tori in various knot types.
The paper classifies all tight contact structures on a solid torus.
problem Classifying tight contact structures on a solid torus with specified dividing sets.
method Writing down a closed formula for the number of non-isotopic tight contact structures with any given dividing set.
result The complete classification of tight contact structures on a solid torus.
Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology optimization, we explore a data-driven approach that can quickly generate accurate so…
In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of …
The problem of classifying, upto isometry (or similarity), the orientable spherical, Euclidean and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. In the spherical and hyperbolic cases, this allows us to complete the classification begun by…
Study on metrics on manifolds with specific curvature properties.
problem Existence of conformal metrics with negative constant scalar curvature and negative constant mean curvature.
method Construction of metrics on smooth manifolds with solid cones removed, proving existence under certain conditions.
result Existence of such metrics if and only if the dimension condition d>(n-2)/2.
Smooth 3D flows from non-smooth starting points.
problem Creating smooth Ricci flows from non-smooth initial conditions.
method Generalized singular Ricci flow applied to 3D complete manifolds.
result Existence of smooth Ricci flows starting from non-smooth initial conditions.
Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.
problem Characterize essential surfaces in Seifert fiber spaces with singular surfaces.
method Extends Frohman and Rannard's approach to handle surfaces with singular fibers.
result Characterizes essential surfaces in Seifert fiber spaces with singular surfaces.
Study shows Heegaard genus relation in 3-manifold amalgamation.
problem Understanding Heegaard genus in 3-manifold amalgamation.
method Examined amalgamation of 3-manifolds, used degree-one maps, and fixed boundary conditions.
result Proved g(M)≥g(N), showing Heegaard genus relation. Given a smooth closed oriented manifold M of dimension n embedded in Rn+2 we study properties of the `solid angle' function Φ:Rn+2∖M→S1. It turns out that a non-critical level set of Φ is an explicit Seifert hypersurface for M.
Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.
problem Understanding IR phases of 3D class R theories associated with non-hyperbolic 3-manifolds.
method Analysis of IR phenomena through `exceptional' Dehn fillings and gauging of flavor symmetries.
result 3D class R theories associated with certain atoroidal non-hyperbolic 3-manifolds exhibit supersymmetry enhancement at low energy.
Weaved helices form mechanically stable 3D structures.
problem Creating stable 3D structures from helical elements.
method Exploiting screw symmetry and invariant cylindrical rod packing to form triply periodic arrangements.
result Demonstrated nineteen triply periodic arrangements of interwoven helices.
Identifies Heegaard Floer homology solid tori via Dehn fillings.
problem Characterizing Heegaard Floer homology solid tori.
method Using Dehn fillings to identify solid tori.
result Characterized Seifert fibered Heegaard Floer solid tori.
Paper computes skein modules of 3-manifolds using braids.
problem Computing skein modules of 3-manifolds.
method Using braids and knot algebras.
result Braid approach to HOMFLYPT and Kauffman bracket skein modules of specific 3-manifolds.
We show that if a hyperbolic 3-manifold M with a single torus boundary admits two Dehn fillings at distance 5, each of which contains an essential torus, then M is a rational homology solid torus, which is not large in the sense of Wu. Moreover, one of the surgered manifold contains an essential torus which meets t…
Study large N oscillations in 3D theories related to black hole physics.
problem Understanding large N sign oscillations in 3D theories via holography.
method Holographic computation of on-shell actions for Euclidean supergravity solutions, Wick rotation of magnetically charged AdS4 black holes.
result Proposed a non-trivial mathematical conjecture regarding phase factors of twisted Reidemeister-Ray-Singer torsion.
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.
This paper classifies all 3D rep-tiles up to homeomorphism.
problem Identifying compact 3D shapes that can be tiled into smaller copies of themselves.
method Examined all 3D rep-tiles up to homeomorphism, showing equivalence to the exterior of a connected graph in S3. result A 3-manifold is a 3D rep-tile if and only if it is the exterior of a connected graph in S3. Identifies 3D-index as invariant for cusped hyperbolic 3-manifolds.
problem Invariance of q-series for cusped hyperbolic 3-manifolds.
method Relates Frohman-Kania-Bartoszynska's q-series to Dimofte-Gaiotto-Gukov's 3D-index and tetrahedron index.
result Topological invariance of Frohman-Kania-Bartoszynska's q-series.
Considering a solid 3-dimensional Klein bottle and a collaring of its boundary, can we extend a generic C∞ non-singular function defined on the collaring to the full solid Klein bottle without critical points? We give a condition on the Reeb graph of the given function that is necessary and sufficient for the e…
This paper refines previous work by the first author. We study the question of which links in the 3-sphere can be obtained as closures of a given 1-manifold in an unknotted solid torus in the 3-sphere (or genus-1 tangle) by adjoining another 1-manifold in the complementary solid torus. We distinguish between even and o…
New proof of wave trace formula for 3D-contact manifolds.
problem Wave trace formula for 3D-contact manifolds.
method Normal form reduction to Heisenberg group.
result Extension of Chazarain-Duistermaat-Guillemin formula.
The abstract discusses constructing 3d N=2 gauge theories using surgeries and M5-branes.
problem Constructing geometrically 3d N=2 gauge theories.
method Using surgeries and M5-branes wrapping on plumbing three-manifolds.
result Various dualities of 3d theories can be interpreted as Kirby moves and equivalent surgeries.
Dimofte, Gaiotto and Gukov introduced a powerful invariant, the 3D-index, associated to a suitable ideal triangulation of a 3-manifold with torus boundary components. The 3D-index is a collection of formal power series in q1/2 with integer coefficients. Our goal is to explain how the 3D-index is a generating serie…
One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N=2 SCFT T[M3] --- or, rather, a "collection of SCFTs" as we refer to it in the paper --- for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgerie…
The paper studies decay near singularities of 3d Yang-Mills-Higgs fields.
problem Understanding isolated singularities of 3d Yang-Mills-Higgs fields.
method Derives decay estimates and applies removable singularity theorems.
result Generalizes removable singularity theorems for 3d Yang-Mills-Higgs fields.
Defines a map connecting 3d-index and skein module.
problem Connecting mathematical physics predictions with topological quantum field theory.
method Defines a map from skein module to Laurent series ring.
result The map fulfills a supersymmetry prediction and is part of a conjectural topological quantum field theory.
Study on high-dimensional solid tori reveals infinite generation in their diffeomorphism groups.
problem Infinite generation in the homotopy groups of high-dimensional solid tori diffeomorphisms.
method Analysis of homotopy fibre of a linearisation map from the plus-construction of the classifying space of certain space of self-embeddings of stabilisations of the manifold to a form of Hermitian K-theory of the integral group ring of π1(S1).
result Homotopy groups of diffeomorphisms of high-dimensional solid tori are infinite in certain degrees.
Python tools for 3D shape analysis on Kendall's space.
problem Lack of practical utilities for advanced 3D shape analysis.
method Developed Python tools for 3D shape analysis on Kendall's 3D Shape Space.
result Efficient, accessible software solutions for researchers.
We show that if a cusped hyperbolic manifold is Platonic, i.e., can be decomposed into isometric Platonic solids, it can also be decomposed into geodesic ideal tetrahedra.
We reconcile between two classical models of edge-dislocations in solids. The first model, dating from the early 1900s models isolated edge-dislocations as line singularities in locally-Euclidean manifolds. The second model, dating from the 1950s, models continuously-distributed edge-dislocations as smooth manifolds en…
We study knots in 3d Chern-Simons theory with complex gauge group SL(N,C), in the context of its relation with 3d N=2 theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d (2,0) theory, which is compactified on a 3-manifold M^. …
3D spaces without boundaries are found that aren't manifolds.
problem Finding compact aspherical Alexandrov spaces without boundaries.
method Constructing specific examples of 3D spaces.
result Examples of 3D spaces without boundaries that are not topological manifolds.
This paper studies certain embedded spheres in closed affine manifolds. For n≥3, we investigate the dome bodies in a closed affine n-manifold M with its boundary homeomorphic to a sphere under the assumption that a developing map restricted to a component of ∂M^ is an embedding onto a strictly …
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant n-discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on two scales: the local scale corresponds to the discretization, the global scale to…