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.