Alexandrov's Approach to the Minkowski Problem

TL;DR

This paper reviews Alexandrov's functional-analytical method for solving the Minkowski problem and applies it to extremal isoperimetric problems with conflicting objectives.

Contribution

It highlights Alexandrov's approach and demonstrates its application to complex extremal problems in convex geometry.

Findings

Alexandrov's method effectively addresses the Minkowski problem.

Application to isoperimetric extremal problems yields new insights.

The approach bridges convex geometry and functional analysis.

Abstract

This article is dedicated to the centenary of the birth of Aleksandr D. Alexandrov (1912-1999). His functional-analytical approach to the solving of the Minkowski problem is examined and applied to the extremal problems of isoperimetric type with conflicting goals.