Related papers: Alexandrov's Approach to the Minkowski Problem
This is a short tribute to Alexandr Alexandrov (1912--1999).
The 150th anniversary of the birth of the outstanding Russian mathematician Vladimir Andreevich Steklov falls on January 9, 2014. In this paper (it is a part of survey to be published in January 2014), we describe advances in one of several…
This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed extensively in recent years. The paper surveys classical and…
The essay is devoted to the personality of the prominent theorist D.V. Volkov and his pioneer works in quantum field theory and elementary particle physics.
The idea of convexity feeds generation, separation, calculus, and approximation. Generation appears as duality; separation, as optimality; calculus, as representation; and approximation, as stability. This is an overview of the origin,…
During the years 1940-1970, Alexandrov and the "Leningrad School" have investigated the geometry of singular surfaces in depth. The theory developed by this school is about topological surfaces with an intrinsic metric for which we can…
In this paper, we study the planar Lp-Minkowski problem for all p, which was introduced by Lutwak [23]. A detailed exploration on solvability and uniqueness will be presented.
We obtain a generalized version of an inequality, first derived by C. Bandle in the analytic setting, for weak subsolutions of a singular Liouville-type equation. As an application we obtain a new proof of the Alexandrov isoperimetric…
This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…
The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike…
In this paper, we generalize a theorem {\`a} la Alexandrov of Wang, Wang and Zhang [WWZ] for closed codimension-two spacelike submanifolds in the Minkowski spacetime for an adapted CMC condition .
In his beautiful paper [1], Ben Andrews obtained the complete classification of the solutions of the planar isotropic $L_p$ Minkowski problem. In this paper, by generalizing Ben Andrews's result we obtain the complete classification of the…
In this paper, we consider the classification problem for critical points of relative isoperimetric-type problem in the half-space. Under certain regularity assumption, we prove an Alexandrov-type theorem for the singular capillary CMC…
The $L_p$ Aleksandrov integral curvature and its corresponding characterization problem---the $L_p$ Aleksandrov problem---were recently introduced by Huang, Lutwak, Yang, and Zhang. The current work presents a solution to the $L_p$…
The following is an exposition of a course of algebra that Prof. Aleksandr Aleksandrovich Zykov (1922-2013) distributed among the participants of his seminar in graph theory not far away from Odessa, Ukraine, on September, 1991. It is a…
The article is a tribute to Hermann Minkowski leading from his geometry of numbers to an attempt at using Finsler geometry for a break of Lorentz invariance.
Recently, the duals of Federer's curvature measures, called dual curvature measures, were discovered by Huang, Lutwak, Yang, and Zhang (ACTA, 2016). In the same paper, they posed the dual Minkowski problem, the characterization problem for…
Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a…
Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D.S. Mitrinovic, who left us 25 years ago. His significant influence to…
This is the opening article of the abstract book of conference "Set-Theoretic Topology and Topological Algebra" in honor of professor Alexander Arhangelskii on the occasion of his 80th birthday held in 2018 at Moscow State University.