What question did this study set out to answer?

The aim is to show the non-total convexity of the Holmes–Thompson area in the hypermetric space $$ ext{ell}^1_4$$.

March 21, 2026Proceedings of the Steklov Institute of Mathematics0 citations

The Holmes–Thompson Area of ¹₄ Is Not Totally Convex

Key Points

The aim is to show the non-total convexity of the Holmes–Thompson area in the hypermetric space $$ ext{ell}^1_4$$.
Mathematical proof addressing properties of the Holmes–Thompson area
Analysis of linear projections in hypermetric spaces
Certain planes in $$ ext{ell}^1_4$$ do not allow for minimizing projections.
Demonstrated that the Holmes–Thompson area is not minimized in these planes.

Abstract

We prove that the Holmes–Thompson area of the hypermetric space ¹₄ is not totally convex. This means that for some planes in this space, there are no linear projections onto them that minimize the Holmes–Thompson area.

KI fragen

Bookmark

View Full Paper