Related papers: Openness and convexity for momentum maps

We define notions of local topological convergence and local geometric convergence for embedded graphs in $\mathbb{R}^n,$ and study their properties. The former is related to Benjamini-Schramm convergence, and the latter to weak convergence…

H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite…

Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays…

In this paper, we extend the scope of Caffarelli's contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probability densities in $\R^d$. Our focus is on a broader category of…

Kirwan identified a condition on a smooth function under which the usual techniques of Morse-Bott theory can be applied to this function. We prove that if a function satisfies this condition locally then it also satisfies the condition…

There is a hierarchy of structure conditions for convex sets. In this paper we study a recently defined [3, 8, 9] condition called locally nonconical convexity (abbreviated LNC). Is is easy to show that every strictly convex set is LNC, as…

We establish the correspondence between two apparently unrelated but in fact complementary approaches of a relativistic deformed kinematics: the geometric properties of momentum space and the loss of absolute locality in canonical…

A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric…

This paper focuses on investigating generalized relative interior notions for sets in locally convex topological vector spaces with particular attentions to graphs of set-valued mappings and epigraphs of extended-real-valued functions. We…

We characterise proper morphisms of $\infty$-topoi in terms of a relativised notion of compactness: we show that a geometric morphism of $\infty$-topoi is proper if and only if it commutes with colimits indexed by filtered internal…

We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of…

In this paper we introduce Hausdorff locally convex algebra topologies on subalgebras of the whole algebra of nonlinear generalized functions. These topologies are strong duals of Fr\'echet-Schwartz space topologies and even strong duals of…

We establish universal approximation theorems for infinite-dimensional geometric rough paths, i.e., we show that continuous functions on the space of infinite-dimensional weakly geometric H\"older continuous rough paths can be approximated…

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…

The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.

This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds…

Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…

We demonstrate that the idempotent barycenter map, associated with a t-norm $\ast$, is open if and only if the map of max-$\ast$ convex combination is open. As a corollary, we deduce that the idempotent barycenter map is open for spaces of…

We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…

For the minimal graph defined on a convex ring in the space form with nonnegative curvature, we obtain the regularity and the strict convexity about its level sets by the continuity method.