Related papers: Semiconcave functions in Alexandrov's geometry

This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…

We discuss various phenomena of tangency in projective and convex geometry.

We give a new characterization of spaces with nonnegative curvature in the sense of Alexandrov.

We obtain a topological and weakly equivariant classification of closed three-dimensional Alexandrov spaces with an effective isometric circle action. As an application of the classification we prove a version of the Borel conjecture for…

In this work, we introduce a new class of non-convex functions, called implicit concave functions, which are compositions of a concave function with a continuously differentiable mapping. We analyze the properties of their minimization by…

It is a review of some results in Odd symplectic geometry related to the Batalin-Vilkovisky Formalism

The Alexandrov Fenchel inequality, a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes, is fundamental in convex geometry. In $\mathbb{R}^{n+1}$, it states: $\int_M\sigma_k d\mu_g \ge…

We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification…

A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.

In this paper, the results of Mei, Wang, Weng and Xia [Math. Z., 2025, MR4911815] on capillary convex bodies are extended to the anisotropic setting. We develop a theory for anisotropic capillary convex bodies in the half-space and…

For the minimal graph with strict convex level sets, we find an auxiliary function to study the Gaussian curvature of the level sets. We prove that this curvature function is a concave function with respect to the height of the minimal…

An adaptive method connected with 3-point Gauss quadrature and 4-point Lobatto quadrature is introduced and investigated for 5-convex functions.

In this article we utilise abstract convexity theory in order to unify and generalize many different concepts from nonsmooth analysis. We introduce the concepts of abstract codifferentiability, abstract quasidifferentiability and abstract…

In this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha,m)-geometrically convex functions which are generalizations of geometric convex functions.

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.

Abstract. In this paper we prove several rigidity theorems related to and including Lytchak's problem. The focus is on Alexandrov spaces with \curv\geq1, nonempty boundary, and maximal radius \frac{\pi}{2}. We exhibit many such spaces that…

This is a write up on some sections of convex geometry, functional analysis, optimization, and nonstandard models that attract the author.

This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…

We prove concavity properties for solutions to anisotropic quasi-linear equations, extending previous results known in the Euclidean case. We focus the attention on nonsmooth anisotropies and in particular we also allow the functions…

Given an affine variety X and a finite dimensional vector space of regular functions L on X, we associate a convex body to (X, L) such that its volume is responsible for the number of solutions of a generic system of functions from L. This…