arXiv research

The study examines minimal surfaces in Riemannian products of surfaces.

Cone structures over minimal products can't be calibrated smoothly.

Verify spiral minimal product structure using Takahashi Theorem.

The study restricts stable minimal immersions in product spaces to specific configurations.

Minimal submanifolds in spheres can be produced via Clifford type minimal products, and their Morse indices and nullities are calculated.

Unstable minimal surfaces in n-space link to hyperbolic products.

Study shows how certain metrics can be split into warped products.

This paper proves area-minimizing cones over products of Grassmannian manifolds.

The study compares and finds Yamabe constants on warped products.

The paper constructs free boundary minimal surfaces in product spaces using eigenvalue methods.

Stable compact minimal submanifolds of the product of a sphere and any Riemannian manifold are classified whenever the dimension of the sphere is at least three. The complete classification of the stable compact minimal submanifolds of the product of two spheres is obtained. Also, it is proved that the only stable comp…

The study classifies stable submanifolds in product spaces of projective spaces.

In this paper, we study multiplicity of solutions of the Yamabe problem on product manifolds with minimal boundary via bifurcation theory.

A general study of minimal surfaces of the Riemannian product of two spheres S^2xS^2 is tackled. We stablish a local correspondence between (non-complex) minimal surfaces of S^2xS^2 and certain pair of minimal surfaces of the sphere S^3. This correspondence also allows us to link minimal surfaces in S^3 and in the Riem…

In a seminal paper published in $1968$, J. Simons proved that, for $n\leq 5$, the Euclidean (minimal) cone $CM$, built on a closed, oriented, minimal and non totally geodesic hypersurface $M^n$ of $\mathbb S^{n+1}$ is unstable. In this paper, we extend Simons' analysis to {\em warped} (minimal) cones built over a close…

Study minimal Kähler submanifolds in product of space forms.

We prove minimal entropy rigidity for complete, finite volume manifolds locally isometric to a product of rank one symmetric spaces of dimension at least 3: the locally symmetric metric uniquely minimizes (normalized) entropy among all Riemannian metrics. The corresponding theorem is true for maps into these spaces as …

We prove that, among metrics on a compact quotient of $\left(\mathbb{H}^2\right)^n$ (product of hyperbolic planes) of prescribed total volume, the product of hyperbolic metrics has minimal volume entropy.

In this paper we prove existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in $\mathbb R^3$. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in Sol3 with a one-param…

The paper studies Einstein-type structures in warped product manifolds.

Paper constructs new minimal submanifolds in spheres by spinning given ones.

In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in product manifolds $M \times \R$, where $M$ is the hyperbolic plane, the Euclidean plane or the two dimensional sphere. The main tool is the existence of a Jacobi field which characterize the property to be foli…

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.

The study finds conditions for area-minimizing cones over submanifolds.

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

New minimal surfaces found in a specific type of 3D space.

Geometrically, tensors of fixed rank form a minimal submanifold.

Study investigates minimal surfaces in spherical caps, extending previous findings.

Study counts minimal Lagrangians in hyperbolic surfaces with precise growth rate.

We investigate minimal surfaces in products of two-spheres ${\mathbb S}^2_p\times {\mathbb S}^2_p$, with the neutral metric given by $(g,-g)$. Here ${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$ , and $g$ is the induced metric on the sphere. We compute all totally geodesic surfaces and we give a relation between minimal …

Researchers solve a Riemannian geometry problem using warped products.

In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds, each having constant sectional curvature. As the main result, we give a complet…

Hasse principle applied to area-minimizing submanifolds across different homology types.

This paper explores twisted Lagrangian tori in C^2 and their Hamiltonian stationarity.

The study examines gradient almost Yamabe solitons in warped product manifolds and their geometric properties.

Study classifies minimal surfaces and solitons in hyperbolic 3-space as translation surfaces.

we construct a properly embedded minimal surface in the flat product R^2*S^1 which is quasi-periodic but is not periodic.

We consider complete noncompact Riemannian manifolds with quadratically decaying lower Ricci curvature bounds and minimal volume growth. We first prove a rigidity result showing that ends with strongly minimal volume growth are isometric to warped product manifolds. Next we consider the almost rigid case in which manif…

In this paper, we prove a classification theorem for the stable compact minimal submanifolds of the Riemannian product of an $m_1$-dimensional ($m_1\geq3$) hypersurface $M_1$ in the Euclidean space and any Riemannian manifold $M_2$, when the sectional curvature $K_{M_1}$ of $M_1$ satisfies $\frac{1}{\sqrt{m_1-1}}\leq K…

Extends isoparametric foliations and area-minimizing cones in product manifolds.

We develop a model characterizing all possible knots and links arising from recombination starting with a twist knot substrate, extending previous work of Buck and Flapan. We show that all knot or link products fall into three well-understood families of knots and links, and prove that given a positive integer $n$, the…

Study on entropy stability in product spaces of negatively curved symmetric spaces.

Study elliptic Weingarten surfaces in warped product space with specific curvature conditions.

Investigates minimal genus of second homology classes in RAAGs, finding bounds and specific cases.

Let $(Σ_1,g_1)$ and $(Σ_2,g_2)$ be connected, complete and orientable Riemannian two manifolds. Consider the two canonical Kähler structures $(G^ε,J,Ω^ε)$ on the product 4-manifold $Σ_1\timesΣ_2$ given by $G^ε=g_1\oplus εg_2$, $ε=\pm 1$ and $J$ is the canonical product complex structure. Thus for $ε=1$ the Kähler metr…

Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces $-$ minimal isoparametric hypersurfaces and focal submanifolds. By virtue of their rich structures, we find new series of minimizing cones. They are cones over focal submanifolds and cones over suitable products among th…

The paper proves a new inequality for submanifolds in Riemannian space forms and applies it to find minimal submanifolds.

We give a complete enumeration of all combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2\times S^1$ and 615 triangulations of the twisted sphere product $S^2_\times_S^1$. All the 3-spheres…