Related papers: Parabolic SL(r)-opers
In the present paper we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients - the cuspidal parabolic subalgebras. We explicate also the maximal…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
Following ideas of Nori, Biswas, ..., we show that given an integer r>0, a noetherian scheme X, and an effective Cartier divisor D on it, the parabolic vector bundles on (X,D) with weights multiples of 1/r (in the sense of…
We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…
A representation theorem for continuous, SL(n) covariant vector-valued valuations on Orlicz spaces is established. Such valuations are uniquely characterized as moment vectors.
We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.
On contact manifolds we describe a notion of (contact) finite-type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite-type in this…
We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.
We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…
The $p$-Laplacian for graphs, as well as the vertex Laplace operator and the hyperedge Laplace operator for the general setting of oriented hypergraphs, are generalized. In particular, both a vertex $p$-Laplacian and a hyperedge…
Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics we…
We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…
We characterize helix surfaces (constant angle surfaces) in the special linear group $\mathrm{SL}(2,\r)$. In particular, we give an explicit local description of these surfaces in terms of a suitable curve and a 1-parameter family of…
Given a Hermitian vector bundle over an infinite weighted graph, we define the Laplacian associated to a unitary connection on this bundle and study the essential self-adjointness of a perturbation of this Laplacian by an operator-valued…
Properties of a parametric curve in R^3 are often determined by analysis of its piecewise linear (PL) approximation. For Bezier curves, there are standard algorithms, known as subdivision, that recursively create PL curves that converge to…
The author studies structure of space $\mathbf{L}_{2}(G)$ of vectors - functions, which are integrable with a square of the module on the bounded domain $G $of three-dimensional space with smooth boundary, and role of the gradient of…
We study vector bundles with some additional structures on an elliptic curve and show how there are related to the elliptic Ruijsenaars-Schneider model.
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.
In the present work we describe 3-dimensional complex SL_2-varieties where the generic SL_2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group…