Hahn-Banach for metric functionals and horofunctions

Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces

We study the horofunction boundaries of Hilbert and Thompson geometries, and of Banach spaces, in arbitrary dimension. By comparing the boundaries of these spaces, we show that the only Hilbert and Thompson geometries that are isometric to Banach spaces are the ones defined on the cone of positive continuous functions on a compact space.

On metric convexity, the discrete Hahn-Banach theorem, separating systems and sets of points forming only acute angles

This text has three parts. The first one is largely autobiographical, hence my use of the first person. There I recall how Gerard Cohen influenced important parts of my research. The second is of a more classic mathematical nature. I present a discrete analogue of the Hahn-Banach theorem, which serves as a basis for generalizing the notion of separating systems in the context of metric convexity. The third one aims at building a bridge between two communities of researchers, those interested in separating systems, and those interested in a certain question in combinatorial geometry --- sets of…

非紧型 Hermitian 对称空间的 horofunction 与度量紧化

Horofunctions and metric compactification of noncompact Hermitian symmetric spaces

本文利用 JB*-triple 实现，完整刻画了非紧型 Hermitian 对称空间在 Carathéodory 距离下的 horofunction，并证明其度量紧化同胚于闭对偶单位球。