arXiv research

In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we obtain a complete classification of homogeneous production functions with two inputs whose production surfaces are developable.

A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the product production functions of 2 variables in terms of the geometry of their a…

The paper modifies a warped product space to find conditions for constant height functions.

In this article we obtain classification results on the quasi-product production functions in terms of the geometry of their associated graph hypersurfaces, generalizing in a new setting some recent results concerning basic production models. In particular, we obtain several results on the geometry of Spillman-Mitscher…

Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to scale. These extensions are needed in order to explain the regularities of the empiri…

Precise computations of Dehn functions for subgroups of free group products.

Heterogeneity of economic agents is emphasized in a new trend of macroeconomics. Accordingly the new emerging discipline requires one to replace the production function, one of key ideas in the conventional economics, by an alternative which can take an explicit account of distribution of firms' production activities. …

The paper proves Schauder estimates on cone products and characterizes harmonic functions.

The purpose of this study is to estimate the production function and examine the structure of production in the mining sector of Iran. Several studies have already been conducted in estimating production functions of various economic sectors; however, less attention has been paid to mining sectors. After examining the …

Mathematically, a homothetic function is a function of the form $f({\bf x})=F(h(x_1,...,x_n))$, where $h$ is a homogeneous function of any degree $d\ne 0$ and $F$ is a monotonically increasing function. In economics homothetic functions are production functions whose marginal technical rate of substitution is homogeneo…

The paper examines conditions for compactness in sequences of warped product length spaces.

New method detects non-product domains using squeezing function.

We prove that complete warped product Einstein metrics with isometric bases, simply connected space form fibers, and the same Ricci curvature and dimension are isometric. In the compact case we also prove that the warping functions must be the same up to scaling, while in the non-compact case there are simple examples …

In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed the effects of normally distributed noise in the production process. Due to its w…

To obtain groups with bounded harmonic functions (which are not hyperbolic), one of the most frequent way is to look at some semi-direct products (\eg lamplighter groups). The aim here is to show that many of these semi-direct products do not admit harmonic functions with gradient in $\ell^p$, for $p\in [1,\infty[$.

The paper proves rigidity for hypersurfaces with constant shifted curvature functions in warped product manifolds.

We characterize Ricci almost solitons on semi-Riemannian warped products, considering the potential function to depend on the fiber or not. We show that the fiber is necessarily an Einstein manifold. As a consequence of our characterization we prove that when the potential function depends on the fiber, if the gradient…

Complete classification of isoparametric hypersurfaces in product spaces of space forms.

The study examines Einstein-Finsler spaces using Minkowskian products.

New rigidity found for 3D warped product domains.

We give explicit formulas for the intertwinors on the scalar functions over the product of spheres with the natural pseudo-Riemannian product metric using the spectrum generating technique. As a consequence, this provides another proof of the even order conformally invariant differential operator formulas obtained earl…

Study on special symmetries in biwarped product 3-manifolds.

In this paper, we study Riemannian functionals defined by $L^2$-norms of Ricci curvature, scalar curvature, Weyl curvature, and Riemannian curvature. We try to understand stability of their critical points that are products of Einstein metrics. In particular, we prove that the product of a spherical space form and a co…

The study defines and constructs hypersurfaces in a product of two space forms.

We discuss conformal deformation and warped products on some open manifolds. We discuss how these can be applied to construct Riemannian metrics with specific scalar curvature functions.

Characterizes warping functions in Einstein Poisson warped spaces.

The GJMS operators of special Einstein products are factored into simpler operators and applied to solve the Q-Yamabe problem.

The paper proves rigidity for submanifolds in warped product manifolds.

Researchers determine Dehn functions of specific nilpotent groups.

We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.

Study on warped product Yamabe solitons with constant fiber curvature.

Adaptive time decay functions improve financial product recommendation accuracy.

We derive one unified formula for Ricci curvature tensor on arbitrary warped product manifold by introducing a new notation for the lift vector and the Levi-Civita connection.This formula is helpful to further consider Ricci flow (RF) and hyperbolic geometric flow (HGF) and evolution equations on warped product manifol…

Game theory helps analyze ESOs/EBIs in production and service sectors.

In this paper, we completely classify the homothetical hypersurfaces having null Gauss-Kronocker curvature in a Euclidean (n+1)-space. Several applications to the production functions in economics are also given.

The paper explores volume product and slicing conjectures using convex body deformations.

The paper classifies hypersurfaces in $\mathbb{H}^2 imes\mathbb{H}^2$ with constant curvature.

Researchers prove inner product recovery is impossible in latent space models.

Researchers find a way to bound the complexity of certain subgroup geometric invariants.

Study star products on Poisson manifolds compatible with reduction.

Study finds solutions to flows by negative curvature powers.

Functional determinant for mixed signature sphere products depends on sphere dimensions and parity.

This study approximates neural network features for modeling relations and attention mechanisms.

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. We obtain a uniqueness result for prescribing the Ricci curvatur…

Based on the proof of Labastida-Mari{ñ}o-Ooguri-Vafa conjecture \cite{lmov}, we derive an infinite product formula for Chern-Simons partition functions, the generating function of quantum $\fsl_N$ invariants. Some symmetry properties of the infinite product will also be discussed.

The paper studies convexity of products of squared Euclidean distances.

Study of mean curvature flows on graphs in warped product manifolds, focusing on behavior at infinity.

Study Einstein warped products with Einstein base and fiber.