arXiv research

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

No proper biharmonic CMC compact hypersurface in a specific warped product space.

Study on Riemannian Poisson warped product spaces and their properties.

The paper classifies isoparametric hypersurfaces in product spaces with different curvatures.

Classifies hypersurfaces with constant curvature in product spaces.

Linear classifiers in product space forms improve scRNA-seq data classification.

The paper classifies λ-biharmonic hypersurfaces in product spaces.

Study on surfaces in product space with curvature inequality.

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

In this article, we continue the work in \cite{GL} and study a normalized hypersurface flow in the more general ambient setting of warped product spaces. This flow preserves the volume of the bounded domain enclosed by a graphical hypersurface, and monotonically decreases the hypersurface area. As an application, the i…

We prove an almost splitting theorem for the warped product space with warped function $f(r)=\cosh\left(r\sqrt{\fracλ{n-2}}\right)$.

The paper proves rigidity for warped product spaces with degenerate ends.

Estimates modes and ridges in mixed Euclidean and directional spaces.

In this note, we show that there is some counterexample for isoperimetric inequality if the condition $(φ')^2-φ"φ\leq 1$ does not hold in warped product space.

Convex learning for diverse invariances in semi-inner-product space.

The paper examines stability of Minkowski inequalities in warped product spaces.

The study proves uniqueness and symmetry of self-similar solutions in warped product spaces.

The paper calculates curvatures in a specific type of warped product space.

Survey on conjugate surfaces in product spaces.

Characterizes warping functions in Einstein Poisson warped spaces.

Economies grow by upgrading the type of products they produce and export. The technology, capital, institutions and skills needed to make such new products are more easily adapted from some products than others. We study the network of relatedness between products, or product space, finding that most upscale products a…

We show the existence of a deformation process of hypersurfaces from a product space $M_1\times R$ into another product space $M_2\times R$ such that the relation of the principal curvatures of the deformed hypersurfaces can be controlled in terms of the sectional curvatures or Ricci curvatures of $M_1$ and $M_2$. In t…

We give lower bounds for the fundamental tone of open sets in minimal submanifolds immersed into warped product spaces of type $N^n \times_f Q^q$, where $f \in C^\infty(N)$. We also study the essential spectrum of these minimal submanifolds.

In this paper, we discuss the Weyl problem in warped product space. We obtain the openness, non rigidity and some applications. These results together with the a priori estimates obtained by Lu imply some existence results. Meanwhile we reprove the infinitesimal rigidity in the space forms.

Stability results for geometric equations in warped product spaces.

Defines semi-symmetric metric connection on super warped products.

Study on Einstein warped spaces with specific connections and curvature properties.

We prove a Simons type formula for submanifolds with parallel mean curvature vector field in product spaces of type $M^n(c)\times\mathbb{R}$, where $M^n(c)$ is a space form with constant sectional curvature $c$, and then we use it to characterize some of these submanifolds.

The study classifies isoparametric and homogeneous hypersurfaces in product spaces.

In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to draw topological conclusions at the end of the paper.

The paper classifies hypersurfaces in product spaces with specific curvature properties and finds that only rotational ones admit almost Ricci solitons.

The paper studies special warped products with a specific connection on super Riemannian manifolds.

In this paper, we deduce some rigidity results in warped product spaces under normal variations of CMC hypersurfaces. In particular, we prove the existence of one-parameter families locally rigid on the spatial fiber of Anti-de Sitter Schwarzschild spacetime and one-parameter families with bifurcation points on the spa…

The study proves a theorem for surfaces using Codazzi operators and investigates parallel mean curvature surfaces.

Study characterizes Einstein metrics in warped product spaces.

Develops higher arity VC theory and characterizes PAC learning in product spaces.

Geometrically describes surfaces with parallel mean curvature in warped product spaces.

The study extends Jacobi-orthogonality to indefinite scalar product spaces.

The paper derives optimal inequalities for bi-slant submanifolds in metallic Riemannian space forms.

The paper studies conformal-biharmonic hypersurfaces in spheres and product spaces.

The paper classifies solitons in a curved product space.

Characterizes totally umbilical hypersurfaces in product spaces.

This paper classifies grim reapers in a specific product space.

Study asymptotic behavior of translators in hyperbolic product space.

The paper studies a new type of submanifolds in product spaces.

The study constructs minimal surfaces in a product space with specific properties.

What are East Africa's industrial opportunities? In this article we explore this question by using the Product Space to study the productive structure of five south-east African countries: Kenya, Mozambique, Rwanda, Tanzania and Zambia. The Product Space is a network connecting products that tend to be exported by the …

The paper classifies various types of hypersurfaces in a product space.