Hilbert Geometry Without Convexity

2020 ◽  
Vol 30 (3) ◽  
pp. 2865-2896
Author(s):  
E. Falbel ◽  
A. Guilloux ◽  
P. Will
Keyword(s):  
Hilbert Geometry

scholarly journals From Funk to Hilbert geometry

2014 ◽  
pp. 33-67
Author(s):  
Athanase Papadopoulos ◽  
Marc Troyanov
Keyword(s):  
Hilbert Geometry

scholarly journals On coarse geometric aspects of Hilbert geometry

2018 ◽  
Vol 187 (4) ◽  
pp. 665-680
Author(s):  
Ryosuke Mineyama ◽  
Shin-ichi Oguni
Keyword(s):  
Hilbert Geometry

scholarly journals ISOMETRIES OF POLYHEDRAL HILBERT GEOMETRIES

2011 ◽  
Vol 03 (02) ◽  
pp. 213-241 ◽  
Author(s):  
BAS LEMMENS ◽  
CORMAC WALSH
Keyword(s):  
Collineation Group ◽  
Isometry Group ◽  
Hilbert Geometry

We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of collineations (projectivities) if and only if the polyhedron is not an n-simplex with n ≥ 2. Moreover, we determine the isometry group of the Hilbert geometry on the n-simplex for all n ≥ 2, and find that it has the collineation group as an index-two subgroup. The results confirm several conjectures of P. de la Harpe for the class of polyhedral Hilbert geometries.

Hilbert Geometry for Strictly Convex Domains

2004 ◽  
Vol 105 (1) ◽  
pp. 29-42 ◽  
Author(s):  
Bruno Colbois ◽  
Patrick Verovic
Keyword(s):  
Convex Domains ◽  
Hilbert Geometry ◽  
Strictly Convex

scholarly journals Lyapunov exponents in Hilbert geometry

2012 ◽  
Vol 34 (2) ◽  
pp. 501-533 ◽  
Author(s):  
MICKAËL CRAMPON
Keyword(s):  
Lyapunov Exponents ◽  
Convex Functions ◽  
Geodesic Flow ◽  
Regularity Property ◽  
Hilbert Geometry

AbstractWe study the Lyapunov exponents of the geodesic flow of a Hilbert geometry. We prove that all of the information is contained in the shape of the boundary at the endpoint of the chosen orbit. We have to introduce a regularity property of convex functions to make this link precise. As a consequence, Lyapunov manifolds tangent to the Lyapunov splitting appear very easily. All of this work can be seen as a consequence of convexity and the flatness of Hilbert geometries.

scholarly journals On the Hilbert geometry of simplicial Tits sets

2015 ◽  
Vol 65 (3) ◽  
pp. 1005-1030 ◽  
Author(s):  
Xin Nie
Keyword(s):  
Hilbert Geometry

The Application of a Portable DMFCs Stack With Fractal Current Collectors Using Hilbert Geometry for a Charger System

2009 ◽  
Author(s):  
Shah-Rong Lee ◽  
Yean-Der Kuan ◽  
Min-Feng Sung ◽  
Jing-Yi Chang ◽  
Shi-Min Lee
Keyword(s):  
Plate Thickness ◽  
Input Voltage ◽  
Bipolar Plate ◽  
Power Balance ◽  
Third Order ◽  
Current Collectors ◽  
Hilbert Geometry ◽  
Direct Methanol ◽  
System Output ◽  
Methanol Fuel Cell

The study develops a portable charger platform that contains a direct methanol fuel cell (DMFC) consisting of a set of planar DMFCs with current collectors, Fractal Hilbert Geometry and a power balance plant (BOP). The third order Hilbert geometry is used for the 35×35 mm2 current collectors. The system output design is set at 5V controlled by a power balance plant applied to 3C low power products. This paper discusses the Methanol feed rate, air flow rate, bipolar plate thickness and power balance plant layout for DMFC performance. To evaluate the reliability and efficiency of the DMFC power source, a data acquisition (DAQ) system connected to a real time monitor is used to assess the current and voltage output from the DMFC system while running different parameters. The results show the current of the charger system obtain 84 mA and 103 mA under 2V and 3V input voltage converters respectively. The transform efficiency for power balance plant is up to about 84% for 3V input voltage converter.

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