Related papers: Convex KKM maps, monotone operators and Minty vari…
Evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar…
We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we…
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
A functional analog of the Klain-Schneider theorem for vector-valued valuations on convex functions is established, providing a classification of continuous, translation covariant, simple valuations. Under additional rotation equivariance…
We revisit and improve joint concavity/convexity and monotonicity properties of quasi-entropies due to Petz in a new fashion. Then we characterize equality cases in the monotonicity inequalities (the data-processing inequalities) of…
Mercer inequality for convex functions is a variant of Jensen's inequality, with an operator version that is still valid without operator convexity. This paper is two folded. First, we present a Mercer-type inequality for operators without…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
We consider monotone mean-variance (MMV) portfolio selection problems with a conic convex constraint under diffusion models, and their counterpart problems under mean-variance (MV) preferences. We obtain the precommitted optimal strategies…
We present the fundamental properties of the K-theory groups of complex vector bundles endowed with actions of magnetic groups. In this work we show that the magnetic equivariant K-theory groups define an equivariant cohomology theory, we…
We study a certain class of piecewise monotonic maps of interval. These maps are strictly monotone on finite interval partition, satisfies Markov condition and have generator property. We show that for a function from this class…
The convexity and Morse-theoretic properties of moment maps in symplectic geometry typically fail for presymplectic manifolds. We find a condition on presymplectic moment maps that prevents these failures. Our result applies for instance to…
We show that for a convex function the following, rather modest conditions, are equivalent to monotonicity under local operations and classical communication. The conditions are: 1)invariance under local unitaries, 2) invariance under…
We prove the existence of equilibrium states for geometric potentials in a class of piecewise weakly convex interval maps. This class includes systems with indifferent fixed points and non-Markov partitions. Under additional hypotheses we…
For a broad class of integral functionals defined on the space of $n$-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn-Minkowski type…
The purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps. It is shown that they are of topological nature; more specifically, we show that convexity follows if the map is open onto…
Inspired in the theorem of Krein-Milamn, we investigate the existence of extreme points in compact convex subsets of asymmetric normed spaces. We focus our attention in the finite dimensional case, giving a geometric description of all…
Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper, we introduce the notion of convexity of M. It implies that the momentum image is convex, the moment map has connected fibers, and the total moment map is open…