Related papers: Extremal length and duality
We define and study odd analogues of classical geometric and combinatorial objects associated to permutations, namely odd Schubert varieties, odd diagrams, and odd inversion sets. We show that there is a bijection between odd inversion sets…
Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum…
We offer an example of the second order Kawaguchi metric function the extremal flow of which generalizes the flat space-time model of the semi-classical spinning particle to the framework of the pseudo-Riemannian space-time. The general…
We show that certain geometrically defined higher codimension cycles are extremal in the effective cone of the moduli space $\overline{\mathcal M}_{g,n}$ of stable genus $g$ curves with $n$ ordered marked points. In particular, we prove…
We study the uniqueness of optimal solutions to extremal graph theory problems. Lovasz conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the…
A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…
We consider the problem of extending a conformal metric of negative curvature, given outside a neighbourhood of 0 in the unit disk $\DD$, to a conformal metric of negative curvature in $\DD$. We give conditions under which such an extension…
We consider two types of fractional integral moduli of smoothness, which are widely used in theory of functions and approximation theory. In particular, we obtain new equivalences between these moduli of smoothness and the classical moduli…
A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as…
The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
The main scalar-mean extremality and rigidity results in the existing literature concern manifolds whose curvature operators are nonnegative, or warped product spaces with a log-concave warping function whose leaves carry metrics of…
Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two…
For $\alpha\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(\xi,|\xi|^\alpha)$. For the corresponding $\alpha$-Strichartz inequalities, by applying the missing mass method and bilinear restriction…
The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the CFT's associated to loop groups, as twisted equivariant K-theory. We build on their work to…
We study the geometry of the smooth projective surfaces that are defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree.…
This survey concerns regular graphs that are extremal with respect to the number of independent sets, and more generally, graph homomorphisms. More precisely, in the family of of $d$-regular graphs, which graph $G$ maximizes/minimizes the…
Left invariant metrics induced by the p-norms of the trace in the matrix algebra are studied on the general lineal group. By means of the Euler-Lagrange equations, existence and uniqueness of extremal paths for the length functional are…
The aim of this paper is to investigate extremum problems with pay-off being the total variational distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures,…
In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1…