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Within the framework of deformation quantization, a first step towards the study of star-products is the calculation of Hochschild cohomology. The aim of this article is precisely to determine the Hochschild homology and cohomology in two…
We introduce a family of spaces, parametrized by positive real numbers, that includes all of the Hirzebruch surfaces. Each space is viewed from two distinct perspectives. First, as a leaf space of a compact, complex, foliated manifold,…
We compute the Hochschild cohomology of Hilbert schemes of points on surfaces and observe that it is, in general, not determined solely by the Hochschild cohomology of the surface, but by its "Hochschild-Serre cohomology": the bigraded…
A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a…
In this paper, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.
The symmetry operators for the Laplacian in flat space were recently described and here we consider the same question for the square of the Laplacian. Again, there is a close connection with conformal geometry. There are three main steps in…
The Sersic law reproduces very well the surface brightness profile of early-type galaxies, and therefore is routinely used in observational and theoretical works. Unfortunately, its deprojection can not be expressed in terms of elementary…
In this short article we show an orthogonal decomposition of a Hilbert space as a sum of null solutions of the first derivative and the first derivative of a traceless higher order Hilbert/Sobolev space. We define orthogonal projections and…
In this paper we prove existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in $\mathbb R^3$. In particular, we obtain these surfaces…
We prove that the complex surfaces parametrizing cuboids and face cuboids, as well as their minimal resolution of singularities, have trivial fundamental group. We then compute the fundamental group of certain open smooth subvarieties of…
General formulas for the construction of exact solutions of the equation of the minimal surface in $R^3$, which appears in various physical problems, have been derived by the Zakharov-Shabat "dressing" method. Particular examples are…
We construct explicit equations of Cartwright-Steger and related surfaces.
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix…
In this paper we study the Dirichlet problem for a class of Hessian type equation with its structure as a combination of elementary symmetric functions on Hermitian manifolds. Under some conditions with the initial data on manifolds and…
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when…
In the minimal surface theory, the Krust theorem asserts that if a minimal surface in the Euclidean 3-space $\mathbb{E}^3$ is the graph of a function over a convex domain, then each surface of its associated family is also a graph. The same…
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition for that algebraic surface having a standard parametric…
In this paper, a well-posed simultaneous space-time First Order System Least Squares formulation is constructed of the instationary incompressible Stokes equations with slip boundary conditions. As a consequence of this well-posedness, the…