Related papers: Formulas for 2-D Beltrami Operators
A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.
We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the three-dimensional Euclidean space and we study surfaces which are of finite type in…
We discuss the following aspects of two-dimensional N=2 supersymmetric theories defined on compact super Riemann surfaces: parametrization of (2,0) and (2,2) superconformal structures in terms of Beltrami coefficients and formulation of…
We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on two-dimensional…
This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…
The convergence problem of the Laplace-Beltrami operators plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve the operator. In this note…
We study on a new kind of surface covered by translation and factorable (TF-type) surfaces in the three dimensional Euclidean space. We consider I and III Laplace-Beltrami operator surfaces of a TF-type surface. Then we obtain degrees and…
We give a survey on the Weierstrass representations of surfaces in three- and four-dimensional spaces, their applications to the theory of the Willmore functional and on related problems of spectral theory of the two-dimensional Dirac…
In this paper, we construct Laplace-Beltrami operators associated with arbitrary Riemannian metrics on noncommutative tori of any dimension. These operators enjoy the main properties of the Laplace-Beltrami operators on ordinary Riemannian…
The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and…
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
In a recent survey paper we introduced one-sided multipliers between two different operator spaces. Here we give some basic theory for these maps.
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
The $i$-th eigenvalue $\lambda_i$ of the Laplace-Beltrami operator on a surface can be considered as a functional on the space of all Riemannian metrics of unit volume on this surface. Surprisingly only few examples of extremal metrics for…
A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…
In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…