Related papers: Quantum Minimal Surfaces

We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.

We introduce canonical principal parameters on any strongly regular minimal surface in the three dimensional sphere and prove that any such a surface is determined up to a motion by its normal curvature function satisfying the Sinh-Poisson…

We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…

In this paper, we construct compact embedded $\lambda$-hypersurfaces with the topology of torus which are called $\lambda$-torus in Euclidean spaces $\mathbb {R}^{n+1}$.

In this paper, we show that any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal. The proof is based on reducing the biharmonic equation to a system of ordinary differential equations for the profile…

In this paper, we investigate surfaces in singular semi-Euclidean space $\mathbb{R}^{0,2,1}$ endowed with a degenerate metric. We define $d$-minimal surfaces, and give a representation formula of Weierstrass type. Moreover, we prove that…

We survey the classification of the Riemannian metrics on spheres with respect to which all equators are minimal hypersurfaces, and discuss problems related to these geometries.

We review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.

In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We classified…

Special class of surfaces in five-dimensional sphere in $C^3$ is considered. Immersion equations for minimal tori of that class are shown to be reducible to the equation $u_{z\bar z}=e^u-e^{-2u}$ which is integrable by means of inverse…

We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.

We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.

The $q$-binomial coefficients are q-analogues of the binomial coefficients, counting the number of $k$-dimensional subspaces in the $n$-dimensional vector space $\mathbb{F}^n_q$ over $\mathbb{F}_{q}$. In this paper, we define a Euclidean…

It is pointed out that the equations $\sum_{i=1}^d [X_i,[X_i,X_j]]=0$ (and its super-symmetrizations, playing a central role in M-theory matrix models) describe noncommutative minimal surfaces -- and can be solved as such.

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.…

We give elementary geometric proofs of the main theorems about the (small) quantum cohomology of partial flag varieties SL(n)/P, including the quantum Pieri and quantum Giambelli formulas and the presentation.

This paper establishes the conditions under which minimal and stable minimal hypersurfaces are characterized as hyperplanes in Euclidean spaces and as totally geodesic submanifolds in Riemannian manifolds.

We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way…

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean $(n+1)-$space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized…

Minimal surfaces in the Riemannian product of surfaces of constant curvature have been considered recently, particularly as these products arise as spaces of oriented geodesics of 3-dimensional space-forms. This papers considers more…