Related papers: On the quantization of some polynomial minimal sur…
An exact quantization of the spherical membrane moving in flat target spacetime backgrounds is performed. Crucial ingredients are the exact integrabilty of the $3D~SU(\infty)$ continuous Toda equation and the quasi-finite highest weight…
New classes of exact M(em)brane solutions in M+2 dimensional Minkowski space are presented (some describing non-trivial topology changes, while others explicitly avoid finite-time singularity formation)
We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.
Classical solutions of membrane equations that were recently identified as limits of matrix-solutions are looked upon from another angle
We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.
Apart from relating interesting quantum mechanical systems to equations describing a parabolic discrete minimal surface, the quantization of a cubic minimal surface in $\mathbb{R}^4$ is considered.
A membrane technique, in which the symplectic and Ricci forms are integrated over surfaces in a complexification of the phase space, as well a ``creation" connection with zero curvature over lagrangian submanifolds, is used to obtain a…
We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.
Hyperplanes, hyperspheres and hypercylinders in $\Bbb R^n$ with suitable densities are proved to be weighted minimizing by a calibration argument. Also calibration method is used to prove a weighted minimal hypersurface is weighted…
We discuss translation minimal surfaces, homothetical minimal surfaces, and separable minimal surfaces in the $3$-space with $2m$-norm.
We show that compatible almost-complex structures on symplectic manifolds correspond to optimal quantizations.
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…
We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we…
An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the…
The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…
In a previous work we have introduced the concept of quasi-integrable quantum system. In the present one we determine sufficient conditions under which, given an integrable classical system, it is possible to construct a quasi-integrable…
A (holomorphic) quantization of a complex contact manifold is a filtered algebroid stack which is locally equivalent to the ring E of microdifferential operators and which has trivial graded. The existence of a canonical quantization has…
We establish an energy quantization for constrained Willmore surfaces, where the constraints are given by area, volume, and total mean curvature, assuming that the underlying conformal structures remain bounded. Furthermore, we show strong…
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…
We show that a sequence of smooth analytic curves of the unit ball of the complex plane, for which the genus is bounded by the area, converges to a lamination in a weak sense.