Related papers: On the quantization of some polynomial minimal sur…

In this conference report, we present a recent field theoretic renormalization group analysis of flat polymerized membranes at three-loop order by the present authors [Phys. Rev. E 105, L012603 (2022)].

We review the literature on the localization transition for the class of polymers with random potentials that goes under the name of copolymers near selective interfaces. We outline the results, sketch some of the proofs and point out the…

This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.

The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important phenomena in a wide range of applications. Mathematically, if…

Based on a simple example, quantization of some 3-spaces is explained.

We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…

The new property of minimal surfaces is obtained in this article.

It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.

We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…

We investigate the quasisymmetric uniformization of a special class of metric surfaces known as paper surfaces, constructed as quotients of planar multipolygons via segment pairings, including infinite Type W identifications. These spaces,…

The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…

The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.

The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on…

Recently, S.~Kanti Patra and Md.~Moid Shaik proved the existence of monochromatic solutions to systems of polynomial equations near zero for particular dense subsemigroups $S$ of $((0,\infty),+)$. We extend their results to a much larger…

We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our…

Computations in the cohomology of finite groups.

We introduce the notion of radical parametrization of a surface, and we provide algorithms to compute such type of parametrizations for families of surfaces, like: Fermat surfaces, surfaces with a high multiplicity (at least the degree…

Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then…

Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first…

In this paper we review recent results by the author on the problem of quantization of measures. More precisely, we propose a dynamical approach, and we investigate it in dimensions 1 and 2. Moreover, we discuss a recent general result on…