Related papers: Constraint maps and free boundaries
This is the expanded notes of the lecture by the author in "Arrangements in Pyrenees", June 2012. We are discussing relations of freeness and splitting problems of vector bundles, several techniques proving freeness of hyperplane…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…
We employ min-max techniques to show that the unit ball in $\mathbb{R}^3$ contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.
We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…
This article makes no claim to originality, other than, perhaps, the simple statement here called the {\it Abstract Maximum Principle}. Actually, the whole contents are strongly based on some H. Sussmann's and coauthors' papers, in which,…
In this short note we will explore some recent connections between positivity, singularities, and boundedness in various contexts focusing on birational geometry.
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
Fine-grained complexity theory is the area of theoretical computer science that proves conditional lower bounds based on the Strong Exponential Time Hypothesis and similar conjectures. This area has been thriving in the last decade, leading…
Short review of experimental and theoretical researches influence of inner boundaries at properties of composite materials. Reviewing articles that are made at the last, approximately, thirty years, and which demonstrate role of inner…
Lately, to provide a solid ground for quantization of the open string theory with a constant B-field, it has been proposed to treat the boundary conditions as hamiltonian constraints. It seems that this proposal is quite general and should…
In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.
A complete set of the Virasoro and W-constraints for the Kontsevich-Penner model, which conjecturally describes intersections on moduli spaces of open curves, was derived in our previous work. Here we show that these constraints can be…
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
Manturov recently introduced the idea of a free knot, i.e. an equivalence class of virtual knots where equivalence is generated by crossing change and virtualization moves. He showed that if a free knot diagram is associated to a graph that…
We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to…
In the present note we study some arrangements of inflectional lines, hyperosculating conics, and a nodal plane cubic that are free. Moreover, we study weak combinatorics of arrangements consisting of lines, conics, and elliptic curves…
This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry…
Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary…
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…