arXiv research

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.

In this paper, we generalize the Hersch-Payne-Schiffer inequality for Steklov eigenvalues to higher dimensional case by extending the trick used by Hersch, Payne and Schiffer to higher dimensional manifolds.

A novel method visualizes higher-dimensional spaces using hyperbolic geometry.

The (abelian bosonic) heterotic string effective action, equations of motion and Bianchi identity at order alpha prime in ten dimensions, are shown to be equivalent to a higher dimensional action, its derived equations of motion and Bianchi identity. The two actions are the same up to the gauge fields: the latter are a…

We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics. The starting point of our investigation is the higher dimensional (infinitesimal) version of Bianchi's main four theorems on the theory of deformations of quadrics and Bianchi's treatment of the …

We define the transgression functor which associates to a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle of the manifold.

This paper concerns some stability properties of higher dimensional catenoids in $\rr^{n+1}$ with $n\ge 3$. We prove that higher dimensional catenoids have index one. We use $δ$-stablity for minimal hypersurfaces and show that the catenoid is $\frac 2n$-stable and a complete $\frac 2n$-stable minimal hypersurface is a …

We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL(2;C)-representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We al…

Researchers find explicit Bäcklund transforms for specific quadrics.

Higher dimensional generalizations of Schwarz's $P$-surface, Schwarz's $D$-surface and Scherk's second surface are constructed as complete embedded periodic minimal hy- persurfaces in $\mathbb R^n$.

Transformed quadrics from 2D to higher dimensions.

We introduce the foliated anti-self dual equation for higher dimensional smooth manifolds with codimension-4 Riemannian foliations. Several fundamental results are established, towards the defining of a Donaldson type invariant for such foliations.

We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the membrane case.

Constructs Gabor frames for curved manifolds to detect boundaries.

The classical Cohn-Vossen theorem states that two isometric compact convex surfaces in $\mathbb{R}^{3}$ are congruent. In this short note, we generalize the classical Cohn-Vossen Theorem to higher dimensional surfaces in space form $N^{n+1}(K)$ for $n\ge 2$.

The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra of polyvector fields as its non-linear cohomology.

Multisections generalize Heegaard splittings and trisections to higher dimensions.

We analyze higher-dimensional sliding puzzles, finding solvability patterns.

This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic n-space for n greater than 3. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and their contrast with the discrete groups of isometry of the hyperbolic 3-space.

We obtain several results for (iterated) planar contact manifolds in higher dimensions: (1) Iterated planar contact manifolds are not weakly symplectically semi-fillable. This generalizes a 3-dimensional result of Etnyre to a higher-dimensional setting. (2) They do not arise as nonseparating weak contact-type hypersurf…

The paper characterizes Eguchi-Hanson space and its higher-dimensional analogs using Lichnerowicz Laplacian.

Computational techniques calculate dimensions of complex structures.

Study on higher-dimensional black holes, focusing on retractions and scalar quasibound states.

Study shows bounded cohomology vanishes for higher dimensional sphere diffeomorphisms.

We show that the absolute value at zero of the Ruelle zeta function defined by the geodesic flow coincides with the higher-dimensional Reidemeister torsion for the unit tangent bundle over a 2-dimensional hyperbolic orbifold and a non-unitary representation of the fundamental group. Our proof is based on the integral e…

We study the problem of prescribing the Paneitz curvature on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of suc…

Develops method to compute Chern-Simons potentials from higher-dimensional Pontryagin densities.

Maximally hyperbolic solutions contain future neighborhoods of intersecting hypersurfaces.

Paper introduces a new operator and solves equations on higher-dimensional almost Kähler manifolds.

In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions, one can restrict to simplicial spheres of particular shapes, called "round" and "u…

Proves gap rigidity theorem for Hermitian symmetric spaces.

We present a Donaldson-Witten type field theory in eight dimensions on manifolds with $Spin(7)$ holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi…

Study on higher-dimensional quasigeodesics in metric spaces.

Study higher-dimensional Ricci flow solutions, proving uniqueness.

We establish a "low rank property" for Sobolev mappings that pointwise solve a first order nonlinear system of PDEs, whose smooth solutions have the so-called "contact property". As a consequence, Sobolev mappings from an open set of the plane, taking values in the first Heisenberg group and that have almost everywhere…

Maps Heegaard Floer homology to Hecke algebras for surfaces.

We construct infinitely many non-diffeomorphic examples of $5$-dimensional contact manifolds which are tight, admit no strong fillings, and do not have Giroux torsion. We obtain obstruction results for symplectic cobordisms, for which we give a proof not relying on the polyfold abstract perturbation scheme for SFT. The…

We bound the higher-order Dehn functions and other filling invariants of certain Carnot groups using approximation techniques. These groups include the higher-dimensional Heisenberg groups, jet groups, and central products of two-step nilpotent groups. Some consequences of this work are a construction of groups with ar…

Sharp gradient estimates extended to surfaces with lower Ricci curvature.

A simplified proof for embedding higher-dimensional complexes into manifolds.

We study the existence of a non-spacelike isometry, ζ, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of constraints for the metric functions in each case. Within the class of N dimensional CSI Ku…

Heegaard Floer homology connects to polynomial representations of Hecke algebras.

The aim of this paper is to describe a large class of Hermitian Gray manifolds.

In this paper, we study solutions to the linearized vacuum Einstein equations centered at higher-dimensional Schwarzschild met- rics. We employ Hodge decomposition to split solutions into scalar, co-vector, and two-tensor pieces; the first two portions respectively cor- respond to the closed and co-closed, or polar and…

In this paper we investigate the higher dimensional divergence functions of mapping class groups of surfaces and of CAT(0)--groups. We show that, for mapping class groups of surfaces, these functions exhibit phase transitions at the rank (as measured by thrice the genus plus the number of punctures minus 3). We also pr…

The configuration space of the reduced Hamiltonian formulation of quantum gravity has been shown, for non-Ricci flat metrics, to be a higher-dimensional analogue of the Teichmüller space of conformal structures on a Riemann surface. In this article we show that the configuration space of conformal connection-dynamics i…

Researchers found a quadratic estimate for embedding higher-dimensional simplices into sphere-connected sums.

Higher-dimensional Milnor frames are characterized and contrasted with 3D Heisenberg and 4D nilpotent Lie algebras.