Asymptotic Volume in Hilbert Geometries

作者：Vernicos Constantin^*

来源：Indiana University Mathematics Journal, 2013, 62(5): 1431-1441.

• Hilbert geometry
• Finsler
• asymptotic volume
• polytopes

We prove that the metric balls of a Hilbert geometry admit a volume growth which is bigger than a polynomial function with degree equal to their dimension. We also characterise the convex polytopes as those convex sets whose Hilbert geometry has polynomial volume growth of order equal to their dimension.

• 出版日期2013