Farthest points on most Alexandrov surfaces

TL;DR

This paper investigates the properties of the farthest points on a broad class of Alexandrov surfaces with curvature constraints, focusing on their global maximum points using Baire category methods.

Contribution

It introduces a novel Baire category approach to analyze farthest points on most Alexandrov surfaces with curvature bounds.

Findings

Characterization of farthest points on generic Alexandrov surfaces

Identification of properties of distance functions' maxima

Insights into the geometry of surfaces with curvature bounds

Abstract

We study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where "most" is used in the sense of Baire categories.