Affine functions on Alexandrov spaces
Christian Lange, Stephan Stadler

TL;DR
This paper demonstrates that finite-dimensional Alexandrov spaces with curvature bounds can be embedded into a product space, where affine functions on the original space correspond to affine functions on Euclidean factors, revealing structural insights.
Contribution
It introduces a canonical embedding of finite-dimensional Alexandrov spaces into product spaces, linking affine functions to Euclidean components, a novel structural result.
Findings
Finite-dimensional Alexandrov spaces embed into product spaces.
Affine functions on these spaces originate from Euclidean factors.
The embedding preserves affine function structures.
Abstract
We show that every finite-dimensional Alexandrov space X with curvature bounded from below embeds canonically into a product of an Alexandrov space with the same curvature bound and a Euclidean space such that each affine function on X comes from an affine function on the Euclidean space.
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