相关论文: Openness and convexity for momentum maps

We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting…

We extend the classical Donaldson-Fujiki interpretation of the scalar curvature as moment map in K\"ahler Geometry to the wider framework of locally conformally K\"ahler Geometry.

The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular…

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…

Let $(A, B)$ be a nonempty bounded closed convex proximal parallel pair in a nearly uniformly convex Banach space and $T: A\cup B \rightarrow A\cup B$ be a continuous and asymptotically relatively nonexpansive map. We prove that there…

For a conformal vector field on a closed, real-analytic, Lorentzian manifold we prove that the flow is locally isometric -- that it preserves a metric in the conformal class on a neighborhood of any point -- or the metric is everywhere…

In this note, we establish the Lipschitz continuity of finite-dimensional globally convex functions on all given balls and global Lipschitz continuity for eligible functions of that type. The Lipschitz constants in both situations draw…

In this paper, we formulate a simple algorithm that detects contours around a region of interest in an image. After an initial smoothing, the method is based on viewing an image as a topographic surface and finding convex and/or concave…

The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems…

Local-to-global principles are spread all-around in mathematics. The classical Cartan-Hadamard Theorem from Riemannian geometry was generalized by W. Ballmann for metric spaces with non-positive curvature, and by S. Alexander and R. Bishop…

A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…

For a large class of metric spaces with nice local structure, which includes Banach-Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local homeomorphism to be a covering projection. We…

In this work, we study a gap phenomenon in locally conformally flat Riemannian manifolds with non-negative Ricci curvature. We construct complete solutions to the Yamabe flow that exhibit instantaneous bounded curvature as they evolve.…

We introduce the concept of shape-regular regression maps as a framework to derive optimal rates of convergence for various non-parametric local regression estimators. Using Vapnik-Chervonenkis theory, we establish upper and lower bounds on…

The exponential map that characterises the flows of vector fields is the key in understanding the basic structural attributes of control systems in geometric control theory. However, this map does not exists due to the lack of completeness…

We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables; with…

We study the connection between cyclic quasi-monotonicity and quasi-convexity, focusing on whether every cyclically quasi-monotone (possibly multivalued) map is included in the normal cone operator of a quasi-convex function, in analogy…

Generalization of Lyapunov convexity theorem is proved for vector measure with values in Banach spaces with unconditional bases, which are q-concave for some $q<\infty.$

Adaptive methods do not have a direct generalization to manifolds as the adaptive term is not invariant. Momentum methods on manifolds suffer from efficiency problems stemming from the curvature of the manifold. We introduce a framework to…

The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these…