| dbo:abstract |
In der Geometrie sind Hilbert-Metriken gewisse Metriken auf beschränkten konvexen Teilmengen des euklidischen Raumes, die das Beltrami-Klein-Modell der hyperbolischen Geometrie verallgemeinern. (de) In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert as a generalization of Cayley's formula for the distance in the Cayley–Klein model of hyperbolic geometry, where the convex set is the n-dimensional open unit ball. Hilbert's metric has been applied to Perron–Frobenius theory and to constructing Gromov hyperbolic spaces. (en) |
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https://www.cambridge.org/core/books/geometric-group-theory/on-hiberts-metric-for-simplices/8F073A50F15A66D00C59D45ADD7034FC https://www.jstor.org/stable/pdf/2323940.pdf%7Cpublisher https://www.youtube.com/watch%3Fv=XE5x5rAK8Hk https://ghostarchive.org/varchive/youtube/20211220/XE5x5rAK8Hk https://zenodo.org/record/2067884 |
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David Hilbert (en) |
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David (en) |
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Hilbert (en) |
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dbc:Metric_geometry |
| rdfs:comment |
In der Geometrie sind Hilbert-Metriken gewisse Metriken auf beschränkten konvexen Teilmengen des euklidischen Raumes, die das Beltrami-Klein-Modell der hyperbolischen Geometrie verallgemeinern. (de) In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert as a generalization of Cayley's formula for the distance in the Cayley–Klein model of hyperbolic geometry, where the convex set is the n-dimensional open unit ball. Hilbert's metric has been applied to Perron–Frobenius theory and to constructing Gromov hyperbolic spaces. (en) |
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Hilbert-Metrik (de) Hilbert metric (en) |
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wikipedia-en:Hilbert_metric?oldid=1077865147&ns=0 |
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