arXiv research

Study identifies prime strongly positive amphicheiral knots with double symmetry.

The metric algebroid proposed by Vaisman (the Vaisman algebroid) governs the gauge symmetry algebra generated by the C-bracket in double field theory (DFT). We show that the Vaisman algebroid is obtained by an analogue of the Drinfel'd double of Lie algebroids. Based on a geometric realization of doubled space-time as …

Study shows flows from double cones remain symmetric, finds non-symmetric example.

We address the issue why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two-forms and four-forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles…

Rotationally symmetric solutions persist after mean curvature flow starts from a double cone.

Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.

Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective g…

We find contact integrable extensions and coverings for the r-th double modified dispersionless Kadomtsev--Petviashvili equation.

Study CMC hypersurfaces in $\mathbb{H}^2 imes\mathbb{H}^2$ with a specific symmetry.

Symmetric graphs flow without singularities on their axis.

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a …

A new method analyzes topological B-model on a torus using doubled geometry.

Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate, co-closed four-form $C$ introduces a dual symplectic structure $\widetilde{B} = *C$ independent of $B$ via the Hodge duality $*$. We show that the doubling of symplectic structures due to the Hodge duality results in two independent classes of nonc…

We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.

We use a new approach that we call unification to prove that standard weighted double bubbles in $n$-dimensional Euclidean space minimize immiscible fluid surface energy, that is, surface area weighted by constants. The result is new for weighted area, and also gives the simplest known proof to date of the (unit weight…

Survey of global geometry for double field theory.

Stability of a special spacetime solution is proven under certain symmetries.

Study $d$-invariants of L-space double branched covers of arborescent links.

The paper proves an infinite double bubble theorem in higher dimensions.

Article studies symmetry in smooth vector bundles using advanced operations.

In the first part of the paper we discuss the current status of the application of the gluing methodology to doubling and desingularization constructions for minimal surfaces in Riemannian three-manifolds. In particular a doubling construction for equatorial spheres in $S^3(1)$ is announced. Aspects of the current unde…

We formulate a kinematical extension of Double Field Theory on a $2d$-dimensional para-Hermitian manifold $(\mathcal{P},η,ω)$ where the $O(d,d)$ metric $η$ is supplemented by an almost symplectic two-form $ω$. Together $η$ and $ω$ define an almost bi-Lagrangian structure $K$ which provides a splitting of the tangent bu…

In the double field theory, gauge symmetries are realized as generalized diffeomorphisms in the doubled spacetime. By consistency of the theory, dependence of tensor fields on the doubled coordinates is strongly constrained. This causes finite transformation law highly complicated, both technically and conceptually. In…

We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifold…

We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and with…

We study the (massless) Dirac operator on a 3-sphere equipped with Riemannian metric. For the standard metric the spectrum is known. In particular, the eigenvalues closest to zero are the two double eigenvalues +3/2 and -3/2. Our aim is to analyse the behaviour of eigenvalues when the metric is perturbed in an arbitrar…

The paper geometrizes N-manifolds using symmetric vector bundles.

We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler metrics with vanishing scalar curvature which are invariant under the conformal action of Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem …

QNNs can't distinguish binary signals from their negations, revealing a new symmetry.

We develop an equivariant min-max theory as proposed by Pitts-Rubinstein in 1988 and then show that it can produce many of the known minimal surfaces in $\mathbb{S}^3$ up to genus and symmetry group. We also produce several new infinite families of minimal surfaces in $\mathbb{S}^3$ proposed by Pitts-Rubinstein. These …

New Langlands duality conjectures for 3-manifold skein modules.

Constructs finite element spaces for $(p,q)$-forms, excluding one subspace.

Constructs minimal hypersurfaces in S^4(1) by doubling equatorial S^3.

Minimal surfaces in spheres constructed from symmetry reductions of ODEs.

LNNs learn Lagrangians without canonical coordinates, conserving energy and relativity.

Study geometric step options with jumps, deriving pricing equations and characterizations.

This is the first of two companion papers in which a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\em Class. Quantum Grav.} \textbf{21}, 2153-2177 and some of their basic proper…

In this paper we study equivariant constrained Willmore tori in the 3-sphere. These tori admit a 1-parameter group of Möbius symmetries and are critical points of the Willmore energy under conformal variations. We show that the associated spectral curve of an equivariant torus is given by a double covering of $\mathbb …

We show that any star-shaped convex hypersurface with constant Weingarten curvature in the deSitter-Schwarzschild manifold is a sphere of symmetry. Moreover, we study an isoperimetric problem for bounded domains in the doubled Schwarzschild manifold. We prove the existence of an isoperimetric surface for any value of t…

Study of knot Floer homology and its relation to Heegaard Floer homology via equivariant surgery.

Detecting essential surfaces in 3-manifolds and orbifolds using character varieties.

Derives stochastic and dissipative dynamics preserving Gibbs measure.

The study finds polynomial upper bounds for singularities in Einstein-scalar field system.

Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.

An L-space is a rational homology 3-sphere with minimal Heegaard Floer homology. We give the first examples of hyperbolic L-spaces with no symmetries. In particular, unlike all previously known L-spaces, these manifolds are not double branched covers of links in S^3. We prove the existence of infinitely many such examp…

Global Double Field Theory is a higher-dimensional generalization of Kaluza-Klein theory.

Deep linear networks oscillate beyond the edge of stability in a predictable manner.

New self-shrinkers with multiple ends constructed by stacking planes.