arXiv research

Study on scalar curvature in wedge spaces with existence and obstruction results.

Curvature estimate for stable free boundary minimal hypersurfaces in wedge-shaped manifolds.

A fake wedge is a diagram of spaces K <- A -> C whose double mapping cylinder is contractible. The terminology stems from the special case A = K v C with maps given by the projections. In this paper, we study the homotopy type of the moduli space D(K,C) of fake wedges on K and C. We formulate two conjectures concerning…

Paper proves inequality for capillary hypersurfaces in a wedge.

Paper equates torsions on wedge singularities.

Consider a financial market in which an agent trades with utility-induced restrictions on wealth. By introducing a general convex-analytic framework which includes the class of umbrella wedges in certain Riesz spaces and faces of convex sets (consisting of probability measures), together with a duality theory for polar…

The study finds minimal hypersurfaces in wedge-shaped manifolds with boundary.

Let $Σ$ be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in $\mathbb R^{n+1}$. Suppose that $Σ$ meets those two hyperplanes in constant contact angles and is disjoint from the edge of the wedge. It is proved that if $\partial Σ$ is embedded for $n=2$, or if $\partialΣ$ is convex…

Decomposes elements in multiplicative multivectors and relates to Lie algebroid cohomology.

CR embeddings in complex spaces for specific Lie groups.

Study anisotropic capillary surfaces in a wedge using generalized Minkowski norms.

Discrete exterior calculus shows natural properties of wedge product and averaging.

Flat minimal hypersurfaces found in wedge-shaped domains.

Study modular geodesics and wedge domains in non-compactly causal symmetric spaces.

We study the spectrum and heat kernel of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold degenerating to a manifold with wedge singularities. Provided the Hodge Laplacians in the fibers of the wedge have an appropriate spectral gap, we give uniform constructions of the resolvent and heat ker…

Mess showed that the genus 2 Torelli group $T_2$ is isomorphic to a free group of countably infinite rank by showing that genus 2 Torelli space is homotopy equivalent to an infinite wedge of circles. As an application of his computation, we compute the homotopy type of the zero locus of any classical genus 2 theta func…

Defines products for fibered corners manifolds, generalizing resolutions.

New internal symmetry found for Lie pair algebra.

We prove that on a compact Sasakian manifold $(M, η, g)$ of dimension $2n+1$, for any $0 \le p \le n$ the wedge product with $η\wedge (dη)^p$ defines an isomorphism between the spaces of harmonic forms $Ω^{n-p}_Δ(M)$ and $Ω^{n+p+1}_Δ(M)$. Therefore it induces an isomorphism between the de Rham cohomology spaces $H^{n-p…

We establish new Calderón reproducing formulas for self-adjoint operators $D$ that generate strongly continuous groups with finite propagation speed. These formulas allow the analysing function to interact with $D$ through holomorphic functional calculus whilst the synthesising function interacts with $D$ through funct…

Geometrodynamics derived from Riemannian manifolds using geospin matrix.

New insights into Khovanov homology complexity and topological structure.

The paper linearizes higher Courant algebroids using jet and differential operators.

Constructs Dirac generating operators for split Courant algebroids.

We obtain a family of matrix integrals which decompose to a product of Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but generally speaking essentially differ from it). We obtain Plancherel formula for Berezin representations for all series of classical groups (for large values of parameters of re…

This paper classifies commutativity spaces for 3-manifold groups.

The study proves a theorem on Riemannian manifolds for wedge products of weakly convergent differential forms.

Characterizes when differential forms have weak exterior derivatives based on limiting behavior of integration over simplices.

Let $M_Σ$ be an $n$-dimensional Thom-Mather stratified space of depth $1$. We denote by $βM$ the singular locus and by $L$ the associated link. In this paper we study the problem of when such a space can be endowed with a wedge metric of positive scalar curvature. We relate this problem to recent work on index theory o…

Examines how irreducibility and rigidity affect digital images.

We define local Hardy spaces of differential forms $h^p_{\mathcal D}(\wedge T^*M)$ for all $p\in[1,\infty]$ that are adapted to a class of first order differential operators $\mathcal D$ on a complete Riemannian manifold $M$ with at most exponential volume growth. In particular, if $D$ is the Hodge--Dirac operator on $…

Wedge Sampling improves tensor completion with nearly-linear sample complexity.

We discuss the Ricci-flat `model metrics' on $\mathbb{C}^2$ with cone singularities along the conic $\{zw=1\}$ constructed by Donaldson using the Gibbons-Hawking ansatz over wedges in $\mathbb{R}^3$. In particular we describe their asymptotic behavior at infinity and compute their energies.

Formula decomposes multiplicative forms on Poisson groupoids into two parts.

Novel analysis of neural networks using geometric algebra and convex optimization.

Algorithm finds characteristic maps over complex shapes.

We characterize N=1 vacua of type II theories in terms of generalized complex structure on the internal manifold M. The structure group of T(M) + T*(M) being SU(3) x SU(3) implies the existence of two pure spinors Phi_1 and Phi_2. The conditions for preserving N=1 supersymmetry turn out to be simple generalizations of …

We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this approach with explicit examples. In particular, we describe a short program to determin…

We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain generating functions for traces of differential operators which we call correlation functions. These correlation functions a…

Johnson has defined a surjective homomorphism from the Torelli subgroup of the mapping class group of the surface of genus $g$ with one boundary component to $\wedge^3 H$, the third exterior product of the homology of the surface. Morita then extended Johnson's homomorphism to a homomorphism from the entire mapping cla…

Let M be one of the projective spaces CP^n, HP^n for n>1 or the Cayley projective plane OP^2, and let LM denote the free loop space on M. Using Morse theory methods, we prove that the suspension spectrum of (LM)_+ is homotopy equivalent to the suspension spectrum of M_+ wedge a family of Thom spaces of explicit vector …

In this note we consider a heat trace expansion on a manifold with wedge-like singularity. We show that there are two terms in the expansion that contain information about the presence of the singularity, namely the logarithmic term $ct^{-1/2}\log t$ and the half power term $bt^{-1/2}$. We also give a geometric express…

This paper extends Witten's holomorphic Morse inequalities to singular spaces.

We prove in this article that given a linearly concave domain $D$ in the projective space $\Bbb{CP}^{n}$, a 1-dimensional comlex analytic set $V$ in $D$, and a meromorphic 1-form $φ$ on $V$, $V$ is a subset of an algebraic variety of $\Bbb{CP}^{n}$ and $φ$ is the restriction to $V$ of an algebraic 1-form on $\Bbb{CP}^{…

Study shows physical drift affects put-call parity enforcement, not just option payoffs.

Bordifications of hyperplane arrangements yield complexes with homotopy type of wedges of spheres.

We define quantum exterior product wedge_h and quantum exterior differential d_h on Poisson manifolds (of which symplectic manifolds are an important class of examples). Quantum de Rham cohomology, which is a deformation quantization of de Rham cohomology, is defined as the cohomology of d_h. We also define quantum Dol…

Let (V,(.,.)) be a pseudo-Euclidean vector space and S an irreducible Cl(V)-module. An extended translation algebra is a graded Lie algebra m = m_{-2}+m_{-1} = V+S with bracket given by ([s,t],v) = b(v.s,t) for some nondegenerate so(V)-invariant reflexive bilinear form b on S. An extended Poincaré structure on a manifo…