arXiv research

Paper equates torsions on wedge singularities.

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…

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

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…

Algorithm finds characteristic maps over complex shapes.

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.

This is an extensive (published) survey on CR geometry, whose major themes are: formal analytic reflection principle; generic properties of Systems of (CR) vector fields; pairs of foliations and conjugate reflection identities; Sussmann's orbit theorem; local and global aspects of holomorphic extension of CR functions;…

New insights into X-ray transform on hyperbolic disk, with functional relations and range characterizations.

Let $E$ be a vector bundle over a suitable differential manifold $M$ and let $\wedge^p E$ denote $p$-exterior product of $E$. Given sections $ω_1,\dots,ω_k$ of $E$ and a section $η$ of $\wedge^p E$, we consider the problem if $η$ can be written in the form $η=\sum ω_i\wedgeγ_i,$ where $γ_i$ are sections of $\wedge^{p…

We show that normalized currents of integration along the common zeros of random $m$-tuples of sections of powers of $m$ singular Hermitian big line bundles on a compact Kähler manifold distribute asymptotically to the wedge product of the curvature currents of the metrics. If the Hermitian metrics are Hölder with sing…

This is the first paper in a series to develop a linear and nonlinear theory for elliptic and parabolic equations on Kähler varieties with mild singularities. Donaldson has established a Schauder estimate for linear and complex Monge-Ampère equations when the background Kähler metrics on $\mathbb{C}^n$ have cone singul…

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

Paper disproves potential singularity models for 3D hypersurfaces in R^4.

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

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…

We study the distribution of the common zero sets of $m$-tuples of holomorphic sections of powers of $m$ singular Hermitian pseudo-effective line bundles on a compact Kähler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles c…

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

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

Flat minimal hypersurfaces found in wedge-shaped domains.

Paper proves inequality for capillary hypersurfaces in a wedge.

The paper classifies energy-minimizing sets in specific domains.

We study the Hamiltonian vector field $v=(-\partial f/\partial w,\partial f/\partial z)$ on $\mathbb C^2$, where $f=f(z,w)$ is a polynomial in two complex variables, which is non-degenerate with respect to its Newton's polygon. We introduce coordinates in four-dimensional neighbourhoods of the "points at infinity", in …

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…

This thesis studies positive scalar curvature metrics on G-proper spaces and pseudomanifolds.

Geometrodynamics derived from Riemannian manifolds using geospin matrix.

A differential 1-form $α$ on a manifold of odd dimension $2n+1$, which satisfies the contact condition $α\wedge (dα)^n \neq 0$ almost everywhere, but which vanishes at a point $O$, i.e. $α(O) = 0$, is called a \textit{singular contact form} at $O$. The aim of this paper is to study local normal forms (formal, analytic …

New insights into Khovanov homology complexity and topological structure.

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…

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

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…

Examines how irreducibility and rigidity affect digital images.

Researchers found a new type of singularity in surface evolution equations.

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

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

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

The paper classifies solutions to a specific Toda system around a singular source.

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…

Improved non-squeezing theorem for calibrated geometries proved.

We consider a $(2q+1)$-dimensional smooth manifold $M$ equipped with a $(q+1)$-dimensional, a priori non-integrable, distribution ${\cal D}$ and a $q$-vector field ${\bf T}=T_1\wedge\ldots\wedge T_q$, where $\{T_i\}$ are linearly independent vector fields transverse to~${\cal D}$. Using a $q$-form $ω$ such that ${\cal …

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

New internal symmetry found for Lie pair algebra.

CR embeddings in complex spaces for specific Lie groups.

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

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…

This paper upgrades Khovanov homology to an L-infinity module structure.

Given a pair of (real or complex) Lie algebroid structures on a vector bundle $A$ (over $M$) and its dual $A^*$, and a line bundle $\module$ such that $\module\otimes\module=(\wedge^{\TOP} A^*\otimes\wedge^{\TOP} T^*M)$, there exist two canonically defined differential operators $\bdees$ and $\bdel$ on $\sections{\wedg…