Related papers: A look on equations describing pseudospherical sur…
In the current relativistic literature there are misleading considerations about some singular surfaces. An accurate geometric analysis allows to settle the question. No physical meaning is attributable to the spatial regions surrounded by…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
Bound, strange, neutral superheavy nuclei, stable against strong decay, may exist. A model effective field theory calculation of the surface energy and density of such systems is carried out assuming vector meson couplings to conserved…
In this chapter, we outline some of the many combinatorial tools developed over the past three decades for studying a pseudo-Anosov diffeomorphism of a surface by analyzing the geometry of its mapping torus. We begin with an overview of the…
The squircle is an intermediate shape between the square and the circle. In this paper, we examine and discuss equations for different types of squircles. We then build upon these 2D shapes to come-up with various 3D surfaces based on…
We give a conformal representation for indefinite improper affine spheres which solve the Cauchy problem for their Hessian equation. As consequences, we can characterize their geodesics and obtain a generalized symmetry principle. Then, we…
We investigate the classical and quantum properties of a system of $SU(N)$ non-Abelian Chern-Simons (NACS) particles. After a brief introduction to the subject of NACS particles, we first discuss about the symplectic structure of various…
In the first part of this paper, the main concern is with smoothness properties of the boundary of the pseudospectrum of a matrix polynomial. In the second part, results are obtained concerning the number of connected components of…
We study the Kepler metrics on Kepler manifolds from the point of view of Sasakian geometry and Hessian geometry. This establishes a link between the problem of classical gravity and the modern geometric methods in the study of AdS/CFT…
The perennial formalism is applied to the real, massive Klein-Gordon field on a globally-hyperbolic background space-time with compact Cauchy hypersurfaces. The parametrized form of this system is taken over from the accompanying paper. Two…
The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with homogenuous Cauchy condition at initial time and with the second order Cauchy condition on the boundary of the semi-plane. A class of inputs…
We give an introduction to the study of algebraic hypersurfaces, focusing on the problem of when two hypersurfaces are isomorphic or close to being isomorphic. Working with hypersurfaces and emphasizing examples makes it possible to discuss…
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data,…
During the eighties several physical models using p-adic numbers were proposed. Particularly various models of p-adic quantum mechanics. As a consequence of this fact several new mathematical problems emerged, among them, the study of…
Positive definite functions on spheres have received an increasing interest in many branches of mathematics and statistics. In particular, the Schoenberg sequences in the spectral representation of positive definite functions have been…
A generalized Camassa-Holm equation, which describes pseudospherical surfaces, is considered. Using geometric methods, it is demonstrated that the equation is geometrically integrable. Additionally, an infinite hierarchy of conservation…
We develop the calculus of superforms as a tool for convex geometry. The formalism is applied to valuations on convex bodies, the Alexandrov-Fenchel inequalities and Monge- Amp\`ere equations on the boundary of convex bodies.
In this article we consider the concept of biharmonicity about the hypersurfaces in the Sasakian space form which is equipped with the Tanaka-Webster connection.
The proximity-effect theory developed by Takahashi and Tachiki for infinite multilayers is applied to multilayer systems with a finite number of layers in the growth direction. The purpose is to investigate why previous applications to…
Cauchy's surface area formula expresses the surface area of a convex body as the average area of its orthogonal projections over all directions. While this tool is fundamental in Euclidean geometry, with applications ranging from geometric…