Paper proves rigidity of certain minimal hypersurfaces in a 5D sphere.
problem Characterizing closed minimal hypersurfaces in a 5D sphere.
method Analyzes mean curvature and principal curvatures to prove rigidity.
result Closed minimal hypersurfaces with constant 3-mean curvature and distinct principal curvatures are isoparametric.
New examples of Schoenflies balls are produced using a 5D approach.
problem Identifying Schoenflies balls that are not standard.
method Using a 5-dimensional perspective, algebraic and geometric handle cancellation.
result New examples of Schoenflies balls not known to be standard are produced.
Article generalizes open book construction for 5D contact pairs.
problem Constructing compatible open books on relative contact pairs.
method Introduces generalized square bridge position for 5D Legendrian links.
result Algorithm constructs relative open book decompositions on relative contact pairs.
The study connects surface geometry in 5D to 4D projections and umbilic curvatures.
problem Understanding the geometry of surfaces in 5D space.
method Relating surfaces in 5D to surfaces in 4D via projections and normal sections, analyzing asymptotic directions and umbilic curvatures.
result Relations between asymptotic directions and umbilic curvatures in 5D surfaces and their counterparts in 4D projections.
New surfaces found in 5D space.
problem Constructing smooth embedded special Legendrian surfaces in \(\mathbb S^5\).
method Combining implicit function theorem, loop algebra-valued meromorphic connections, and character variety analysis.
result First genus > 1 embedded special Legendrian surfaces in \(\mathbb S^5\).
Paper characterizes a special hypersurface in 5D sphere.
problem Characterizing minimal hypersurfaces in S5. method Analyzes hypersurfaces satisfying a specific curvature condition.
result Closed minimal hypersurfaces in S5 satisfying a certain curvature condition are either totally geodesic or congruent to the Cartan minimal hypersurface. The paper confirms the existence of 5D regular static vacuum solutions with multiple black holes and Kasner asymptotics.
problem Existence of 5D regular static vacuum solutions with multiple black holes.
method Construction of specific examples with different horizon topologies and analysis of spacetime properties.
result Existence of 5D vacuum solitons with Kasner asymptotics and regular static space-periodic spacetimes.
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…
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 θ=π (SU(2)θ=π YM), by turning on backg…
We continue our research work started in "Kinematic Quantities and Raychaudhuri Equations in a 5D Universe" (Eur. Phys. J. C, 2015), and obtain in a covariant form, the equations of motion with respect to the (1+1+3) threading of a 5D universe (Mˉ,gˉ). The natural splitting of the tangent bundle of $…
New G2-holonomy manifolds from 5d N=1 theories domain walls.
problem Geometrizing domain walls in 5d N=1 theories.
method Constructing 7-manifolds by fibering a Calabi-Yau over a real line.
result 7-manifolds with G2-holonomy from domain walls in 5d theories. GyroSwin models plasma turbulence with neural nets, reducing costs and capturing neglected nonlinearities.
problem Understanding plasma turbulence in fusion reactors, which impairs confinement and limits reactor design.
method Introduces GyroSwin, a scalable 5D neural surrogate that approximates 5D nonlinear gyrokinetic simulations.
result GyroSwin outperforms reduced models in heat flux prediction and captures turbulent energy cascade.
Novel gauge-theoretic Floer homologies defined from 5d N=2 theory, linking 4, 3, and 2-manifolds.
problem Defining and linking novel Floer homologies for different manifold dimensions.
method Physics of a topologically-twisted 5d N=2 gauge theory, Vafa-Witten, Hitchin, and BF configurations.
result Derived novel gauge-theoretic and symplectic Floer homologies, and Atiyah-Floer correspondences.
5D SCFTs can have confining vacua with strings and unbroken symmetries.
problem Investigating phases of 5D SCFTs by varying couplings.
method Using geometric realisation of M-theory on metrically conical Calabi-Yau threefolds.
result Many 5D SCFTs have couplings leading to massive, confining vacua with strings and unbroken symmetries.
Inequality found for a specific equation on 5D manifolds.
problem Finding an inequality for a Yamabe type equation on 5D manifolds.
method Analyzing a Yamabe type equation in 5D manifolds.
result An inequality of type sup x inf found for the Yamabe type equation in 5D.
The study classifies all compact 5D polytopes with 9 facets.
problem Classifying compact hyperbolic Coxeter polytopes.
method Complete classification through mathematical analysis.
result A complete list of compact hyperbolic Coxeter 5D polytopes with 9 facets.
Paper shows rigidity of rotationally symmetric minimal hypersurfaces in 5D spaces.
problem Understanding rigidity of rotationally symmetric minimal hypersurfaces in 5D spaces.
method Pointwise hypersurface invariant analysis for minimal hypersurfaces in spaces of constant curvature.
result Rotationally symmetric minimal hypersurfaces in 5D spaces are rigid.
New algebraic rules for 5D shapes based on 3D cocycles.
problem Creating rules for 5D shapes.
method Using simplicial 3-cocycles to parameterize heptagon relations.
result Parameterized heptagon relations for 5D shapes.
There are two different approaches to exhibit submaximal symmetric rank 2 distributions in 5D via Monge equations. In this note we establish precise relations between these models, find auto-equivalences of one family, and treat two special equations.
Paper derives a formula for renormalized area of minimal hypersurfaces in 5D Poincaré-Einstein spaces.
problem Calculating the renormalized area of minimal hypersurfaces in 5D Poincaré-Einstein spaces.
method Derives a Gauss-Bonnet formula for renormalized area in terms of scalar invariants and characterizes minimal hypersurfaces in terms of conformal geometry.
result Derives a formula expressing renormalized area in terms of integrals of scalar Riemannian invariants.
Neural surrogates speed up 5D gyrokinetic simulations of plasma turbulence.
problem Expensive numerical simulations of plasma turbulence hinder fusion reactor design.
method Trained a hierarchical vision transformer in 5D to predict plasma quantities faster.
result Neural surrogates predict plasma quantities two orders of magnitude faster than numerical codes.
5D AI model detects bad loans without biased features, improving consumer protection.
problem Detecting bad loans without biased features and improving consumer protection.
method Machine learning, BiMOPT features, European Banking Authority principles, AI principles, historical and validation datasets.
result 5D correctly detected 1,461 bad loans out of 1,613 (Sensitivity = 0.91, Prevalence = 0.0253, Positive Predictive Value = 0.19).
Extract anomalies from 5D SCFTs using extra-dimensional η-invariants.
problem Anomalies in quantum field theories.
method Use extra-dimensional η-invariants to bypass traditional blowup techniques.
result Anomalies can be determined directly from η-invariants of asymptotic boundaries.
The paper generalizes knot invariants and their connections to quivers and ideals.
problem Understanding knot complements and their invariants.
method Generalizing FK invariants, knots-quivers correspondence, and A-polynomials; associating FK to branch of A-polynomial; quiver generating series; R-matrices; quantum a-deformed A-polynomial; 3d-5d theory. result Explicit expressions for FK invariants and their quiver representations for several simple knots. In 5D, integrability is linked to curvature constraints of subconformal structures.
problem Dispersionless integrability in 5D partial differential equations.
method Relating integrability to curvature constraints of subconformal structures.
result In 5D, integrability is characterized by the vanishing of a certain curvature of the subconformal structure.
Deep reinforcement learning has shown its success in game playing. However, 2.5D fighting games would be a challenging task to handle due to ambiguity in visual appearances like height or depth of the characters. Moreover, actions in such games typically involve particular sequential action orders, which also makes the…
We give an explicit construction of vertex-transitive tight triangulations of d-manifolds for d≥2. More explicitly, for each d≥2, we construct two (d2+5d+5)-vertex neighborly triangulated d-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated …
In this paper we use the anholonomic frames method to construct exact solutions for vacuum 5D gravity with metrics having off-diagonal components. The solutions are in general anisotropic and possess interesting features such as an anisotropic warp factor with respect to the extra dimension, or a gravitational scaling/…
The 'anholonomic frame' method (see gr-qc/0005025, gr-qc/0001060 and hep-th/0110250) is applied for constructing new classes of exact solutions of vacuum Einstein equations with off-diagonal metrics in 4D and 5D gravity. We examine several black tori solutions generated by anholonomic transforms with non-trivial topolo…
New geometric approach realizes 5D bulk theories with 4D edge modes.
problem Realizing novel higher-dimensional junctions of theories coupled to localized edge modes.
method M-theory on singular, asymptotically conical G2-holonomy orbifolds.
result Geometric approach shows how bulk generalized symmetries are inherited in the boundary system.
Paper classifies structures on 5D manifolds with specific rank and conditions.
problem Classifying tangent distributions on 5D manifolds.
method Established necessary and sufficient topological condition for existence.
result Classification of structures up to homotopy as formal Cartan distributions.
A new algebraic method extracts symmetry anomalies from 5D SCFTs.
problem Extracting global symmetry anomalies from 5D superconformal field theories.
method Path algebra of branes probing Calabi-Yau cones provides a complementary approach.
result Combinatorial approach to symmetry anomalies in 5D SCFTs.
We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as "differential" …
5D gauge theories are dual to 3D and 2D models via Floer homologies.
problem Exploring dualities in 5D gauge theories and their 3D and 2D counterparts.
method Using Landau-Ginzburg models and Floer homologies, the paper establishes dualities between different gauge theories and their associated homologies.
result Dual A∞-categories of Floer homologies are derived, proving mirror symmetry and Langlands duality. The paper finds solutions for specific curvature conditions on 5D Lie groups.
problem Finding metrics with prescribed Ricci curvature on 5D nilpotent Lie groups.
method Applied Milnor-type theorem technique to prove global existence of (g, c).
result Global existence of (g, c) for prescribed Ricci curvature on 5D nilpotent Lie groups.
A 5D manifold's rigidity proven for k=3 with constant scalar curvature.
problem Proving rigidity for a specific case of a quasi-Einstein manifold.
method Analyzing a 5D quasi-Einstein manifold with constant scalar curvature and boundary conditions.
result The case k=3 is rigid, with a specific scalar curvature formula.
Study h-cobordisms of complexity 2 in 5D, finding obstructions and examples.
problem Understanding h-cobordisms of complexity 2 in 5D. method Compute monopole Floer homology and action of twisting involution.
result Obtained obstructions and constructed examples of high complexity.
4D self-shrinkers in 5D space are rigid.
problem Characterizing 4D complete self-shrinkers in 5D space.
method Analyzing the second fundamental form and its components.
result 4D complete self-shrinkers with specific properties are isometric to R^4.
Paper proves existence of minimum energy solutions in 5D contact spin manifolds.
problem Finding minimum energy solutions for CR Yamabe equation in 5D contact spin manifolds.
method Spinorial approach based on a positive mass theorem.
result Existence of minimum energy solutions in 5D contact spin manifolds.
Study of 5D SYM theory on toric surfaces yields refined Vafa-Witten invariants.
problem Computing partition functions in 5D SYM theory on toric surfaces.
method Supersymmetric localization, Nekrasov partition functions, moduli space of sheaves.
result Found correspondence between poles and torus-fixed points in moduli space, leading to refined Vafa-Witten invariants.
In this paper, we propose a deep reinforcement learning (DRL) solution to the grasping problem using 2.5D images as the only source of information. In particular, we developed a simulated environment where a robot equipped with a vacuum gripper has the aim of reaching blocks with planar surfaces. These blocks can have …
The paper derives curvature identities for 5D and 6D Einstein manifolds.
problem Deriving curvature identities for specific dimensions of Einstein manifolds.
method Using Patterson's curvature identities and the Chern-Gauss-Bonnet Theorem, the paper provides explicit formulae for 5D and 6D Einstein manifolds.
result The curvature identities for 5D and 6D Einstein manifolds are confirmed to be consistent with previous work.
We create a minimal triangulation of 5D real projective space.
problem Tackling the minimal triangulation of 5D real projective space.
method Constructing a 6-dimensional polytope with a highly symmetric automorphism group.
result Our construction uses the fewest number of vertices (24) for a triangulation of 5D real projective space.
We construct a new class of exact solutions describing spacetimes possessing Lie algebroid symmetry. They are described by generic off-diagaonal 5D metrics embedded in bosonic string gravity and possess nontrivial limits to the Einstein gravity. While we focus on nonholonomic vielbein transforms of the Schwarzschild me…
In this paper we apply the anholonomic frames method developed in refs. [1-4] to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off--diagonal 5D metric, parameterized in terms of several ansatz functions, we show that using anholonomic frames greatly simplifies the resulting…
Paper classifies Schouten-like metrics on 5D nilpotent Lie groups.
problem Finding Riemannian metrics with prescribed Ricci curvature.
method Introduced Schouten-like metrics and classified them on 5D nilpotent Lie groups.
result Comprehensive classification of 5D nilpotent Lie groups' Schouten-like metrics.
Derive K-theoretic Donaldson invariants for various 4-manifolds using path integrals and topological twists.
problem Calculate K-theoretic Donaldson invariants for different 4-manifolds.
method Topological twisting of 5d Yang-Mills theory, integration over Coulomb branch, equivariant localization.
result Agree with previous results for algebraic surfaces and derive new invariants for more general manifolds.
The article examines how many stabilizations are needed to transform 5D s-cobordisms into product cobordisms.
problem Understanding the number of stabilizations required to convert 5D s-cobordisms into product cobordisms.
method Utilizes Gabai's 4D light bulb theorem and Freedman Quinn invariant.
result Determines the number of stabilizations needed for 5D s-cobordisms.