Related papers: Convex valuations, from Whitney to Nash
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
In this paper we describe a well-chosen discrete moving frame and their associated invariants along projective polygons in $\RP^n$, and we use them to write explicit general expressions for invariant evolutions of projective $N$-gons. We…
We prove the existence and uniqueness of strong solutions to the steady isentropic compressible Navier-Stokes equations with inflow boundary conditions for density and mixed boundary conditions for the velocity around a shear flow. In…
The classification of continuous, translation invariant Minkowski valuations which are contravariant (or covariant) with respect to the complex special linear group is established in a 2-dimensional complex vector space. Every such…
After 1-point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative…
This is the fourth part in the series of articles math.MG/0503397, math.MG/0503399, math.MG/0509512 where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations introduced in…
We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…
We consider an initial-boundary value problem for the $n$-dimensional wave equation with the variable sound speed, $n\geq 1$. We construct three-level implicit in time and compact in space (three-point in each space direction) 4th order…
We study optimal transport-based distributionally robust optimization problems where a fictitious adversary, often envisioned as nature, can choose the distribution of the uncertain problem parameters by reshaping a prescribed reference…
The connection between constraint languages and clone theory has been a fruitful line of research on the complexity of constraint satisfaction problems. In a recent result, Cohen et al. [SICOMP'13] have characterised a Galois connection…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint…
Given a diagram D of a knot K, we give easily computable bounds for Rasmussen's concordance invariant s(K). The bounds are not independent of the diagram D chosen, but we show that for diagrams satisfying a given condition the bounds are…
Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…
We study the inhomogeneous cosmological evolution of the Newtonian gravitational 'constant' G in the framework of scalar-tensor theories. We investigate the differences that arise between the evolution of G in the background universes and…
The smooth (resp. metric and complex) Nielsen Realization Problem for K3 surfaces $M$ asks: when can a finite group $G$ of mapping classes of $M$ be realized by a finite group of diffeomorphisms (resp. isometries of a Ricci-flat metric, or…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
In the area of symbolic-numerical computation within computer algebra, an interesting question is how "close" a random input is to the "critical" ones, like the singular matrices in linear algebra or the polynomials with multiple roots for…
In this paper we identify the problem of equivariant vortex counting in a $(2,2)$ supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov-Witten invariants of the GIT quotient target…
The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on their properties that are essential for actually working…