3 papers
math.MG2026
On the monotonicity of magnitude functions of negative type finite semimetric spaces
Kiyonori Gomi, Hiroshi Tsuji
Motivated by the conjectured monotonicity of the magnitude functions of metric spaces of negative type, we investigate the monotonicity problem for finite semimetric spaces, namely…
math.MG2025
Geometric interpretation of magnitude
Yasuhiko Asao, Kiyonori Gomi
For an positive definite symmetric matrix with for all , we show that there exists a set of vectors such that the radius $…
math.MG2025
Magnitude and matrix inequalities
Kiyonori Gomi, Mark Meckes
We present several applications of matrix-theoretic inequalities to the magnitude of metric spaces. We first resolve an open problem by showing that the magnitude of any finite met…