arXiv research

Study anisotropic obstacle problem for minimal surfaces using Cahn-Hoffman transform.

The paper defines and explores anti-orthotomics of frontals and their applications.

We study the stability of closed, not necessarily smooth, equilibrium surfaces of an anisotropic surface energy for which the Wulff shape is not necessarily smooth. We show that if the Cahn Hoffman field can be extended continuously to the whole surface and if the surface is stable, then the surface is, up to rescaling…

Anisotropic obstacle problems and Stefan problem studied with evolving surfaces.

Generative x-vectors improve SV performance.

New inequalities for subGaussian vectors, tighter than before.

Paper transforms torse-forming vector fields into simpler forms.

Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice, remain constant along the orbits of the `surface' Killing vector. Alternatively, the…

New pushforward operation on vector pseudo-bundles creates new examples.

The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold $M$. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …

For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that the canonical vector field of every Euclidean submanifold is alwa…

Paper finds conditions for finite-dimensional vector spaces of cross-sections.

Study biharmonic vector fields and unit vector fields on Riemannian manifolds.

Characterizes spacetimes using doubly torqued vectors.

Abstract: Generalizes multisymplectic forms to vector-valued versions.

Every smooth vector field is a combination of gradient fields.

The paper bounds the mean absolute error in DNN vector-to-vector regression.

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth famil…

Defines quaternionic k-vector fields on quaternionic Kähler manifolds.

SVM generalizes well even with many support vectors in high dimensions.

Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.

Study on vector fields on Lie groups reveals surprising algebraic coincidences.

Classifies equivariant vector bundles over toric manifolds.

We prove the classification of the real vector subspaces of a quaternionic vector space by using a covariant functor which, to any pair formed of a quaternionic vector space and a real subspace, associates a coherent sheaf over the sphere.

This paper introduces $\infty$- and $n$-fold vector bundles as special functors from the $\infty$- and $n$-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of $n$-fold vector bundles and we prove that any $n$-fold vector bundle admits a non-canonical isomorphism to a decomposed …

Conformal vector fields on LCP manifolds are orthogonal and Killing.

Study on generalized derivations in polynomial vector fields Lie algebras.

Characterizes affine vector fields on Finsler manifolds with rigidity results.

Study on Einstein solitons with specific vector fields and their properties.

Study of generalized vector bundles and their geometric tools.

In this paper we show that for an invariant $(α,β)-$metric $F$ on a homogeneous Finsler manifold $\frac{G}{H}$, induced by an invariant Riemannian metric $\tilde{a}$ and an invariant vector field $\tilde{X}$, the vector $X=\tilde{X}(H)$ is a geodesic vector of $F$ if and only if it is a geodesic vector of $\tilde{a}$. …

The paper explores MAE as a loss function for DNN vector-to-vector regression, proving its advantages over MSE.

SL(n) covariant valuations on Orlicz spaces are represented and characterized.

Defines connections on parabolic vector bundles for Lie algebroids.

Investigates point spectra of vector fields and their properties.

Study describes lcK structures on Vaisman-type manifolds with holomorphic Lee vector field.

Proves GAGA-style result for toric vector bundles.

We explore under what conditions one can obtain a nontrivial knot, given a collection of $n$ vectors. First, we show how to get a crossing from any 3 vectors equal in magnitude, by arbitrarily picking 2 vectors and identifying the sufficient and necessary criteria for picking a third vector that will guarantee a crossi…

We consider four dimensional lie groups equipped with left invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. We also classify vector fields de…

Examining singularities of commuting vector fields on submanifolds.

The paper proves non-existence of torqued and anti-torqued vector fields on hyperbolic spaces.

We introduce G_2-vector fields, Rochesterian 1-forms and Rochesterian vector fields on manifolds with a closed G_2-structure as analogues of symplectic vector fields, Hamiltonian functions and Hamiltonian vector fields respectively, and we show that the spaces of G_2-vector fields and of Rochesterian vector fields are …

This paper explores sentence vector properties for automatic summarization.

Study classifies harmonic vector fields on 3-manifolds.

Proves every equivariant vector bundle over toric manifolds is a Klyachko bundle.

PAC-Bayes analysis explains sentence vector learning from unlabeled data.

Criteria for lifting manifold diffeomorphisms to vector bundle automorphisms.