Related papers: On a convexity problem
In [G. Bianchi, R. J. Gardner and P. Gronchi, Symmetrization in Geometry, Adv. Math., vol. 306 (2017), 51-88], a systematic study of symmetrization operators on convex sets and their properties is conducted. In the end of their article, the…
Clarified certain points and related it to other work.
We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems,…
Two conjectures recently proposed by one of the authors are disproved
A fundamental paper of Elliott Lieb from 1973 has been the basis for much beautiful work on matrix inequalities by many people over the following years. We review a well-connected set of these developments. Some new proofs are provided.
A comment on a recent paper (PRL {\bf 94}, 226405 (2005)) by S. De Palo, M. Botti, S. Moroni, and Gaetano Senatore.
This paper is the continuation of the previous two papers with the same title.
Some inequalities for different types of convexity are established.
The authors mention work of Christensen, Mycielski, Tsujii, and others which is closely related to a survey article by the first author [math.FA/9210220].
We have reviewed the comment in [3], posted on arXiv.org concerning our recent work in [1]. We reply to the comment in this paper.
Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…
We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of…
Comment on the paper "Novel Convective Instabilities in a Magnetic Fluid" by W. Luo, T. Du, and J. Huang, Phys. Rev. Lett., v.82, p.4134 (1999).
The notions of quasiconvexity, Wright convexity and convexity for functions defined on a metric Abelian group are introduced. Various characterizations of such functions, the structural properties of the functions classes so obtained are…
We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
In this paper, approximate convexity and approximate midconvexity properties, called $\varphi$-convexity and $\varphi$-midconvexity, of real valued function are investigated. Various characterizations of $\varphi$-convex and…
This talk is a write-up on some origins of abstract convexity and afew vexing limitations on the range of abstraction in convexity.
In this note we examine the volume of the convex hull of two congruent copies of a convex body in Euclidean $n$-space, under some subsets of the isometry group of the space. We prove inequalities for this volume if the two bodies are…
Comment on paper "Towards a bulk theory of flexoelectricity" by R.Resta [Phys.Rew. Lett. v. 105, 127601 (2010)]